Question

A spider can walk at a certain speed and run at another speed. If he walks for 10 seconds and runs for 9 seconds ,he travels 85m. If he walks for 30 seconds and runs for 2 seconds, he travels 130m. Find his walking and running speeds

Answer 1

Let \( w \) be the walking speed in meters per second and \( r \) be the running speed in meters per second.

From the problem statement, we can derive two equations based on the distance traveled during walking and running:

1. For the first scenario (walking for 10 seconds and running for 9 seconds):
\[
10w + 9r = 85
\]

2. For the second scenario (walking for 30 seconds and running for 2 seconds):
\[
30w + 2r = 130
\]

Now we have the system of equations:
\[
\begin{align*}
10w + 9r &= 85 \quad (1) \\
30w + 2r &= 130 \quad (2)
\end{align*}
\]

We can solve this system of equations using substitution or elimination. Let's use the elimination method.

First, let's multiply the first equation by 2 to make it easier to eliminate \( r \):
\[
20w + 18r = 170 \quad (3)
\]

Now we can multiply the second equation by 9:
\[
270w + 18r = 1170 \quad (4)
\]

Next, we subtract equation (3) from equation (4) to eliminate \( r \):
\[
(270w + 18r) - (20w + 18r) = 1170 - 170
\]
\[
250w = 1000
\]
Divide both sides by 250:
\[
w = 4
\]

Now that we have \( w \), we can substitute \( w = 4 \) back into equation (1) to find \( r \):
\[
10(4) + 9r = 85
\]
\[
40 + 9r = 85
\]
\[
9r = 85 - 40
\]
\[
9r = 45
\]
Divide both sides by 9:
\[
r = 5
\]

Thus, the walking speed \( w \) is 4 m/s and the running speed \( r \) is 5 m/s.

The final answer is:
- Walking speed: **4 m/s**
- Running speed: **5 m/s**