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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 -

    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 -

    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 ??
    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 !!!

  • math -

    A kayak was reduced from $750 to $600, what percentage was it reduced?

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