Running at an average rate of 4 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and the jog back was 2 minutes 6 seconds. Find the length of the track
To find the length of the track, we can start by calculating the time it took the sprinter to run to the end of the track.
Let's assume the length of the track is "x" meters.
The sprinter ran at an average rate of 4 meters per second, so the time taken to run to the end of the track is x/4 seconds.
Next, we need to calculate the time it took the sprinter to jog back to the starting point.
The sprinter jogged back at an average rate of 2 meters per second, so the time taken to jog back to the starting point is x/2 seconds.
The total time for the sprint and the jog back is given as 2 minutes 6 seconds, which can be converted to seconds as 126 seconds.
So we have the equation: x/4 + x/2 = 126
To solve this equation, we can multiply both sides by 4 to remove the denominator:
x + 2x = 504
Combining like terms, we get:
3x = 504
Dividing both sides by 3, we find:
x = 168
Therefore, the length of the track is 168 meters.