Posted by **Michelle ** on Tuesday, October 6, 2009 at 11:44pm.

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?

- math -
**DrBob222**, Wednesday, October 7, 2009 at 12:04am
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.

- math -
**Reiny**, Wednesday, October 7, 2009 at 12:06am
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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