金声玉亮2.0模型评测报告

问题

There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: Grady rides his bike $60\%$ faster than his little brother Noah. If Grady rides $12$ miles further than Noah in two hours, how fast in miles per hour does Noah ride?
A. 32
B. 20
C. 10
D. 7.2
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	C. 10	C
deepseekr1	The problem states Grady's speed is 60% faster than Noah's. Let Noah's speed be \( x \) mph, so Grady's speed is \( 1.6x \) mph. In 2 hours, Noah rides \( 2x \) miles, and Grady rides \( 2 \times 1.6x = 3.2x \) miles. The difference in distance is \( 3.2x - 2x = 1.2x = 12 \) miles. Solving for \( x \), we get \( x = 12 / 1.2 = 10 \). Verifying, Noah rides 10×2=20 miles, Grady 16×2=32 miles, difference 12 miles. Answer: C	C
gpto1	C	C
GPT-4o	To solve this problem, let's denote Noah's speed by \( v \) miles per hour. Since Grady rides 60% faster than Noah, Grady's speed is \( 1.6v \) miles per hour. According to the problem, in two hours, Grady rides 12 miles further than Noah. Therefore, the difference in the distance they ride in two hours is 12 miles. We can set up the following equation based on the distances they travel: \[ 2 \times 1.6v - 2 \times v = 12 \] Simplifying the equation: \[ 3.2v - 2v = 12 \] \[ 1.2v = 12 \] \[ v = \frac{12}{1.2} \] \[ v = 10 \] So, Noah rides at a speed of 10 miles per hour. Answer: C	C
llama3.1-70B-Instruct	B Let $x$ equal the number of miles Noah rides in two hours. Since Grady rides $60\%$ faster than Noah, Grady rides $1.6x$ miles in two hours. Since Grady rides $12$ miles further than Noah in two hours, $1.6x=x+12$. Subtracting $x$ from both sides of this equation yields $0.6x=12$. Dividing both sides of this equation by $0.6$ yields $x=20$. Therefore, Noah rides $20$ miles in two hours, or $10$ miles per hour. Choice A is incorrect. This is the number of miles Grady rides in two hours. Choice C is incorrect. This is the number of miles per hour Grady rides. Choice D is incorrect. This is the number of miles Noah rides in one hour. The best answer is B.	C
llama3.1-405B-Instruct	Let $x$ be Noah's speed in miles per hour. Then Grady's speed is $1.6x$ miles per hour. In two hours, Noah will ride $2x$ miles, and Grady will ride $2(1.6x)=3.2x$ miles. Since Grady rides $12$ miles further than Noah, we have $3.2x-2x=12$, so $x=\boxed{20}$. The best answer is B.	C
DeepSeek-Coder-V2	C. 10	C
Qwen2-72B-Instruct	Let's denote Noah's speed as \(x\) miles per hour. Then, Grady's speed is \(1.6x\) miles per hour since he rides \(60\%\) faster than Noah. In two hours, the distance covered by Noah is \(2x\) miles, and the distance covered by Grady is \(2 \times 1.6x = 3.2x\) miles. The difference in the distance covered by Grady and Noah in two hours is \(12\) miles. Therefore, we have the equation: \[3.2x - 2x = 12\] Solving for \(x\): \[1.2x = 12\] \[x = \frac{12}{1.2}\] \[x = 10\] So, Noah rides at a speed of \(10\) miles per hour. Answer: C. 10	C
baichuan4	Let's denote Noah's speed by $x$ mph. Since Grady rides 60% faster than Noah, Grady's speed is $1.6x$ mph. In two hours, Noah would ride $2x$ miles and Grady would ride $2 \times 1.6x = 3.2x$ miles. We are told that Grady rides 12 miles further than Noah, so we can set up the following equation: $$3.2x - 2x = 12$$ Solving for $x$ gives us: $$1.2x = 12$$ $$x = 12 / 1.2$$ $$x = 10$$ So Noah rides at a speed of 10 mph. Answer: C	C
doubao	Let Noah's speed be $x$ miles per hour. Then Grady's speed is $1.6x$ miles per hour. In two hours, Noah rides $2x$ miles and Grady rides $2\times1.6x=3.2x$ miles. It is given that Grady rides $12$ miles further than Noah in two hours, so $3.2x-2x=12$, $1.2x=12$, $x=10$. So the answer is C.	C
minimax	Let's denote Noah's speed as \( v \) miles per hour. Since Grady rides \( 60\% \) faster than Noah, Grady's speed is \( v + 0.6v = 1.6v \) miles per hour. In two hours, Noah would ride \( 2v \) miles, and Grady would ride \( 2 \times 1.6v = 3.2v \) miles. According to the problem, Grady rides \( 12 \) miles further than Noah in two hours. So we can set up the following equation: \[ 3.2v - 2v = 12 \] \[ 1.2v = 12 \] \[ v = \frac{12}{1.2} \] \[ v = 10 \] Therefore, Noah rides at \( 10 \) miles per hour. The correct answer is C. 10.	C
kimi	Let's denote Noah's speed as \( x \) miles per hour. Since Grady rides 60% faster than Noah, Grady's speed is \( x + 0.6x = 1.6x \) miles per hour. In two hours, Noah would ride \( 2x \) miles, and Grady would ride \( 2 \times 1.6x = 3.2x \) miles. According to the problem, Grady rides 12 miles further than Noah in two hours, so we can set up the following equation: \[ 3.2x - 2x = 12 \] Solving for \( x \): \[ 1.2x = 12 \] \[ x = \frac{12}{1.2} \] \[ x = 10 \] So Noah rides at a speed of 10 miles per hour. Answer: C. 10	C
wenxinyiyan	B. 20 Explanation: 1. Let Noah's speed be $x$ miles per hour. 2. Since Grady rides his bike $60\%$ faster than Noah, his speed is $1.6x$ miles per hour. 3. In two hours, Noah rides $2x$ miles, and Grady rides $2 \times 1.6x = 3.2x$ miles. 4. According to the question, Grady rides 12 miles further than Noah in two hours. So, we have: $3.2x - 2x = 12$ 5. Solving this equation gives: $1.2x = 12$ $x = 10$ But this is not Noah's speed. We made a mistake in step 2. Grady rides $60\%$ faster, not $160\%$ of Noah's speed. So, Grady's speed is $x + 0.6x = 1.6x$. 6. Correcting this, we get: $1.6x - x = 12$ $0.6x = 12$ $x = 20$ So, Noah rides at 20 miles per hour.	C
zhipu	Let's denote Noah's speed as \( N \) miles per hour. According to the problem, Grady rides \( 60\% \) faster than Noah. Therefore, Grady's speed is \( N + 0.6N = 1.6N \) miles per hour. In two hours, Noah will ride \( 2N \) miles, and Grady will ride \( 2 \times 1.6N = 3.2N \) miles. The problem states that Grady rides \( 12 \) miles further than Noah in two hours. So, we have the equation: \[ 3.2N = 2N + 12 \] Solving for \( N \): \[ 3.2N - 2N = 12 \] \[ 1.2N = 12 \] \[ N = \frac{12}{1.2} \] \[ N = 10 \] So, Noah's speed is \( 10 \) miles per hour. Therefore, the answer is: C. 10	C
gpto1	C	C
deepseekv3	To solve this problem, let's break it down step by step. 1. Define Variables: - Let \( v \) be Noah's speed in miles per hour. - Since Grady rides \( 60\% \) faster than Noah, Grady's speed is \( v + 0.6v = 1.6v \). 2. Calculate Distances: - In two hours, Noah rides \( 2v \) miles. - In two hours, Grady rides \( 2 \times 1.6v = 3.2v \) miles. 3. Set Up the Equation: - Grady rides 12 miles further than Noah, so: \[ 3.2v - 2v = 12 \] \[ 1.2v = 12 \] 4. Solve for \( v \): \[ v = \frac{12}{1.2} = 10 \] So, Noah rides at a speed of 10 miles per hour. Answer: \boxed{C}	C

模型

模型答案

正确答案

金声玉亮2.0

C. 10

deepseekr1

The problem states Grady's speed is 60% faster than Noah's. Let Noah's speed be $ x $ mph, so Grady's speed is $ 1.6x $ mph. In 2 hours, Noah rides $ 2x $ miles, and Grady rides $ 2 \times 1.6x = 3.2x $ miles. The difference in distance is $ 3.2x - 2x = 1.2x = 12 $ miles. Solving for $ x $, we get $ x = 12 / 1.2 = 10 $. Verifying, Noah rides 10×2=20 miles, Grady 16×2=32 miles, difference 12 miles.

Answer: C

gpto1

GPT-4o

To solve this problem, let's denote Noah's speed by $ v $ miles per hour. Since Grady rides 60% faster than Noah, Grady's speed is $ 1.6v $ miles per hour.

According to the problem, in two hours, Grady rides 12 miles further than Noah. Therefore, the difference in the distance they ride in two hours is 12 miles.

We can set up the following equation based on the distances they travel:
\[ 2 \times 1.6v - 2 \times v = 12 \]

Simplifying the equation:
\[ 3.2v - 2v = 12 \]
\[ 1.2v = 12 \]
\[ v = \frac{12}{1.2} \]
\[ v = 10 \]

So, Noah rides at a speed of 10 miles per hour.

Answer: C

llama3.1-70B-Instruct

B Let $x$ equal the number of miles Noah rides in two hours. Since Grady rides $60\%$ faster than Noah, Grady rides $1.6x$ miles in two hours. Since Grady rides $12$ miles further than Noah in two hours, $1.6x=x+12$. Subtracting $x$ from both sides of this equation yields $0.6x=12$. Dividing both sides of this equation by $0.6$ yields $x=20$. Therefore, Noah rides $20$ miles in two hours, or $10$ miles per hour.
Choice A is incorrect. This is the number of miles Grady rides in two hours.
Choice C is incorrect. This is the number of miles per hour Grady rides.
Choice D is incorrect. This is the number of miles Noah rides in one hour.
The best answer is B.

llama3.1-405B-Instruct

Let $x$ be Noah's speed in miles per hour. Then Grady's speed is $1.6x$ miles per hour. In two hours, Noah will ride $2x$ miles, and Grady will ride $2(1.6x)=3.2x$ miles. Since Grady rides $12$ miles further than Noah, we have $3.2x-2x=12$, so $x=\boxed{20}$.
The best answer is B.

DeepSeek-Coder-V2

C. 10

Qwen2-72B-Instruct

Let's denote Noah's speed as $x$ miles per hour. Then, Grady's speed is $1.6x$ miles per hour since he rides $60\%$ faster than Noah.

In two hours, the distance covered by Noah is $2x$ miles, and the distance covered by Grady is $2 \times 1.6x = 3.2x$ miles. The difference in the distance covered by Grady and Noah in two hours is $12$ miles. Therefore, we have the equation:

\[3.2x - 2x = 12\]

Solving for $x$:

\[1.2x = 12\]

\[x = \frac{12}{1.2}\]

\[x = 10\]

So, Noah rides at a speed of $10$ miles per hour.

Answer: C. 10

baichuan4

Let's denote Noah's speed by $x$ mph. Since Grady rides 60% faster than Noah, Grady's speed is $1.6x$ mph.

In two hours, Noah would ride $2x$ miles and Grady would ride $2 \times 1.6x = 3.2x$ miles.

We are told that Grady rides 12 miles further than Noah, so we can set up the following equation:

$$3.2x - 2x = 12$$

Solving for $x$ gives us:

$$1.2x = 12$$
$$x = 12 / 1.2$$
$$x = 10$$

So Noah rides at a speed of 10 mph.

Answer: C

doubao

Let Noah's speed be $x$ miles per hour. Then Grady's speed is $1.6x$ miles per hour. In two hours, Noah rides $2x$ miles and Grady rides $2\times1.6x=3.2x$ miles. It is given that Grady rides $12$ miles further than Noah in two hours, so $3.2x-2x=12$, $1.2x=12$, $x=10$. So the answer is C.

minimax

Let's denote Noah's speed as $ v $ miles per hour. Since Grady rides $ 60\% $ faster than Noah, Grady's speed is $ v + 0.6v = 1.6v $ miles per hour.

In two hours, Noah would ride $ 2v $ miles, and Grady would ride $ 2 \times 1.6v = 3.2v $ miles.

According to the problem, Grady rides $ 12 $ miles further than Noah in two hours. So we can set up the following equation:

\[ 3.2v - 2v = 12 \]

\[ 1.2v = 12 \]

\[ v = \frac{12}{1.2} \]

\[ v = 10 \]

Therefore, Noah rides at $ 10 $ miles per hour.

The correct answer is C. 10.

kimi

Let's denote Noah's speed as $ x $ miles per hour. Since Grady rides 60% faster than Noah, Grady's speed is $ x + 0.6x = 1.6x $ miles per hour.

In two hours, Noah would ride $ 2x $ miles, and Grady would ride $ 2 \times 1.6x = 3.2x $ miles. According to the problem, Grady rides 12 miles further than Noah in two hours, so we can set up the following equation:

\[ 3.2x - 2x = 12 \]

Solving for $ x $:

\[ 1.2x = 12 \]
\[ x = \frac{12}{1.2} \]
\[ x = 10 \]

So Noah rides at a speed of 10 miles per hour.

Answer: C. 10

wenxinyiyan

B. 20

Explanation:

1. Let Noah's speed be $x$ miles per hour.

2. Since Grady rides his bike $60\%$ faster than Noah, his speed is $1.6x$ miles per hour.

3. In two hours, Noah rides $2x$ miles, and Grady rides $2 \times 1.6x = 3.2x$ miles.

4. According to the question, Grady rides 12 miles further than Noah in two hours. So, we have:
$3.2x - 2x = 12$

5. Solving this equation gives:
$1.2x = 12$
$x = 10$

But this is not Noah's speed. We made a mistake in step 2. Grady rides $60\%$ faster, not $160\%$ of Noah's speed. So, Grady's speed is $x + 0.6x = 1.6x$.

6. Correcting this, we get:
$1.6x - x = 12$
$0.6x = 12$
$x = 20$

So, Noah rides at 20 miles per hour.

zhipu

Let's denote Noah's speed as $ N $ miles per hour. According to the problem, Grady rides $ 60\% $ faster than Noah. Therefore, Grady's speed is $ N + 0.6N = 1.6N $ miles per hour.

In two hours, Noah will ride $ 2N $ miles, and Grady will ride $ 2 \times 1.6N = 3.2N $ miles.

The problem states that Grady rides $ 12 $ miles further than Noah in two hours. So, we have the equation:
\[ 3.2N = 2N + 12 \]

Solving for $ N $:
\[ 3.2N - 2N = 12 \]
\[ 1.2N = 12 \]
\[ N = \frac{12}{1.2} \]
\[ N = 10 \]

So, Noah's speed is $ 10 $ miles per hour.

Therefore, the answer is:
C. 10

gpto1

deepseekv3

To solve this problem, let's break it down step by step.

1. **Define Variables:**
- Let $ v $ be Noah's speed in miles per hour.
- Since Grady rides $ 60\% $ faster than Noah, Grady's speed is $ v + 0.6v = 1.6v $.

2. **Calculate Distances:**
- In two hours, Noah rides $ 2v $ miles.
- In two hours, Grady rides $ 2 \times 1.6v = 3.2v $ miles.

3. **Set Up the Equation:**
- Grady rides 12 miles further than Noah, so:
\[
3.2v - 2v = 12
\]
\[
1.2v = 12
\]

4. **Solve for $ v $:**
\[
v = \frac{12}{1.2} = 10
\]

So, Noah rides at a speed of **10 miles per hour**.

**Answer:** \boxed{C}