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
t and (126 -t)
4 t = 2 (126-t)
solve for t
then
d = 4 t or d = 2(126 - t)
378?
To find the length of the track, we can use the formula for speed: Speed = Distance / Time.
First, let's find the time it took for the sprint and the jog back. The total time is given as 2 minutes and 6 seconds, which can be converted to seconds as follows:
2 minutes = 2 * 60 seconds = 120 seconds
6 seconds
Therefore, the total time is 120 seconds + 6 seconds = 126 seconds.
Now, let's calculate the time it took for the sprint. We can use the formula Time = Distance / Speed.
The average speed during the sprint was given as 4 meters per second. Let's assume the distance of the track is D. Therefore, the time taken for the sprint is:
Time for sprint = D / 4
Next, let's calculate the time it took for the jog back. The average speed during the jog back was given as 2 meters per second. The distance covered during the jog back is also D. Therefore, the time taken for the jog back is:
Time for jog back = D / 2
According to the problem, the total time for the sprint and the jog back is 2 minutes 6 seconds, which we already converted to 126 seconds.
Now we can create an equation: Time for sprint + Time for jog back = Total time
(D/4) + (D/2) = 126
To solve this equation, we can multiply through by the common denominator, which is 4:
(D/4) * 4 + (D/2) * 4 = 126 * 4
Simplifying, we get:
D + 2D = 504
Combining like terms:
3D = 504
Dividing both sides by 3:
D = 504 / 3
Calculating, we find:
D = 168
Therefore, the length of the track is 168 meters.