John and Mary leave their house at the same time and drive i

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?

Solution

John DATA:
Distance= x+35 miles ; rate= 60 mi/hr ; time = d/r = (x+35)/60
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Mary DATA:
Distance = x miles ; rate= 40 mi/hr ; time = d/r = x/40 hr
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EQUATION:
Mary\'s time - John\'s time = (1/4) hr.
(x/40)-(x+35)/60 = (1/4)
Multiply thru by 4 to get:
=x/10 - (x+35)/15 = 1
Multiply thru by 150 to get
15x-10x-350 = 150
5x=500
x=100
Mary\'s time = 100/40 = 2.5 hr.
John\'s time = (135/60) =2.25 hr.