Question 743648
John and Mary leave their house at the same time  and drive in opposite directions. John drives at 60 mph and travels 35 mi farther than Mary, who drives at 40 mph. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?

let Mary travel x miles
Mary speed = 40 mph
Mary's time = x/40

John will drive x+35 miles
John speed = 60 mph
john's time = (x+35)/60

Mary's time - John's time = 1/4 hour

x/40 - (x+35)/60 = 1/4

LCD = 120
multiply eqn by 120
3x-2(x+35)=30

3x-2x-70=30
x-70=30
x=100 miles=> distance driven by Mary

distance driven by John = 135

Time taken by Mary = 100/40 = 2.5 hours

Time taken by John =135/60 = 2.25 hours