Question 222250
Please help me solve the word problem:  Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track jan is given a 25m head start, and the race ends in a tie.  How long is the track?


Let the length of the track be T


Since Jan’s speed is 7.5 m/s, and since she was given a 25 m head start, then her distance to the finish line is T - 25, and her time to get to the finish line is {{{(T - 25)/7.5}}} secs.


Now, since Mary ran the entire length of the track, and since Mary’s speed is 8 m/s, then Mary’s time to get to the finish line is {{{T/8}}} secs.


Since they finished tied, then they both arrived at the finish line at the same time, which gives us: {{{(T - 25)/7.5 = T/8}}} 

   
8(T – 25) = 7.5T ------ Cross-multiplying


8T – 200 = 7.5T


8T – 7.5T = 200


.5T  =  200


T  = {{{200/.5}}} = 400


This means that the track is a {{{highlight_green(400)}}} meter track.