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
Let's denote the length of the track as "L" meters.
We know that the sprinter ran to the end of the track at an average rate of 4 meters per second, so the time taken for the sprint is given by:
Time for sprint = L / 4 seconds
Similarly, when the sprinter jogged back to the starting point at an average rate of 2 meters per second, the time taken for the jog is given by:
Time for jog = L / 2 seconds
According to the given information, the total time for the sprint and the jog back is 2 minutes 6 seconds, which is equivalent to 126 seconds:
Total time = Time for sprint + Time for jog
126 seconds = (L / 4) + (L / 2)
Now, let's solve the equation for L:
(L / 4) + (L / 2) = 126
Multiply both sides by 4 to eliminate the fractions:
L + 2L = 504
3L = 504
Divide both sides by 3 to isolate L:
L = 504 / 3
L = 168
Therefore, the length of the track is 168 meters.
To find the length of the track, we will first calculate the time it took for the sprinter to run to the end of the track and back.
Let's assume the length of the track is 'x' meters.
To calculate the time taken for the sprint, we can use the formula:
Time = Distance / Speed
The distance covered in the sprint is the entire length of the track 'x'. The speed of the sprinter is 4 meters per second. So the time taken for the sprint is:
Time for sprint = x / 4
To calculate the time taken for the jog back, we can use the same formula:
Time for jog back = x / 2
The total time for the sprint and the jog back is given as 2 minutes 6 seconds, which can be converted to seconds as:
Total time = (2 minutes * 60 seconds per minute) + 6 seconds = 126 seconds
Therefore, the equation becomes:
Time for sprint + Time for jog back = Total time
(x / 4) + (x / 2) = 126
To solve this equation, we need to eliminate the fractions by multiplying through by 4:
(4 * x) / 4 + (4 * x) / 2 = 4 * 126
Simplifying, we get:
x + 2x = 504
Combining like terms:
3x = 504
Dividing both sides by 3:
x = 168
Hence, the length of the track is 168 meters.
since time = distance/speed,
d/4 + d/2 = 126
Now just solve for d