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.