math
posted by Michelle on .
How long will it take a bus traveling at 60 miles per hour to overtake a car traveling at 40 mph if the car had a 1.5 hour head start?

distance = rate x time
Let t = time bus travels
then t+1.5 hours = time car travels
60t = distance traveled by bus.
40(t+1.5) = distance traveled by car.
distance traveled by bus = distance by car.
60t = 40(t+1.5)
solve for time, then use
d = rt to determine the distance. 
let the time it takes for the bus to catch up to the car be t hours
So the bus went 60t miles
but meantime, the car went for t+1.5 hours at 40 mph for a distance of 40(t+1.5
But when the bus catches up to the car, haven't both gone the same distance ??
so
60t = 40(t+1.5)
60t = 40t + 60
20t = 60
t = 3
so it will take 3 hours
check: in 3 hours the bus went 3(6) = 180 miles
the car went for 4.5 hrs at 40 = 180 miles
Checks out !!! 
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