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