how to do this?

Question

running the marathon ( 26.2 miles long)
Thina average speed maintained per mile is 11 min. and 15 sec. She is closer to the front and leaves the starting point at 8:02 a.m.
Manuel is farther behind at the start and he begins his run at 8:15 a.m. Manuel maintains an average speed of 5.8 miles per hour.
How long and at what distance(if it happens) will the 2 be at the same location. and at what time will both kids finish the run?

i need help understanding how to do it

Answer 1

Hello,

let td = Thina distance so td = 60/11.25 t
let md = Manuel distance so md = 5.8 *(t -13/60) since he stars 13 minutes later.

Now to meet they must travel the same distance so
60/11.25t = 5.8(t-13/60) then 5 1/3t = 5.8t - 75.4/60 so then

- .467t = - 75.4/60 then t = 2.69 hours Which will be 2.69 * 60/11.25 = 14.35 miles.

They should meet in approx. 2.69 hours or about 2 hrs. 41 mins.

Now Thina will run 26.2 miles at 60/11.25 miles per hour taking her 4.9 hours and Manuel 26.2 at 5.8 = 4.5 hours.


Check my math Please.
Hope This Helps!!