Question 972951
Running at an average rate of 8 m/s, a sprinter ran to the end of a track and then jogged back to the starting point at an average rate of 3 m/s.
 The sprinter took 55 s to run to the end of the track and jog back.
 Find the length of the track
:
let d = the length of the track in meters
:
Write a time equation. time = dist/speed
:
run time + jog back time = 55 sec
{{{d/8}}}} + {{{d/3}}} = 55
multiply equation by the least common multiple of 8 and 3
24*{{{d/8}}}} + 24*{{{d/3}}} = 24(55)
cancel the denominators
3d + 8d = 1320
11d = 1320
d = 1320/11
d = 120 meters is the length of the track
:
;
:
Confirm this by finding the actual time each way
120/8 = 15 sec
120/3 = 40 sec
---------------
tot time: 55 sec