SOLUTION: John and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Mary's trip ta

Question 732123: John and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
john and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. 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
john travels x+35 miles
John speed = 90 mph
Mary 40 mph
Time Mary = x/40
Time john = (x+35)/90

Time Mary -1/4 = Time John
x/40 - 1/4 = (x+35)/90
x/40-(x+35)/90 = 1/4
90x-40(x+35)= 900
90x-40x-1400=900
90x-40x-1400=900
50x=2300

x=46 miles
John time = (46+35)/90 = 0.9 hours
Mary time = 46/40=1.15 hours

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
John and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?
***
let x=John's travel time
15 min=1/4 hr
(x+1/4)=Mary's travel time
distance=travel time*speed
..
90x-40(x+1/4)=35
90x-40x-10=35
50x=45
x=45/50=9/10 hr or 54 min
x+1/4=18/20+5/20=23/20 hr or 69 min
John's travel time=54 min
Mary's travel time=69 min
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