algebra 2

Kate can row a boat 10 miles per hour in still water. in a river where the current is 5 miler per hour, it take her 4 hour longer to row a given distance upstream than to travel the same distance downstream. Find how long it takes her to row upstream, how long to row downstream, and how many miles she rows.

please help/ thank you.

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  1. rate against the current = 10-5 = 5 mph
    rate with the current = 10+5 = 15 mph

    let the distance be x

    time against the current = x/5
    time with the current = x/15

    x/5 - x/15 = 4
    times 15
    3x - x = 60
    2x = 60
    x = 30

    each way is 30 miles
    time upstream = 30/5 = 6 hrs
    time downstream = 30/15 = 2 hrs
    (note the difference is 4 hrs, as it should be)

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