math algebra. i need help!?

A boat can travel 10 miles downstream in 70 minutes.The return trip upstream requires 2 hours. Find the rate of the boat and the rate of the current. PLEASE INCLUDE THE WORKING. THANK YOU!

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  • 1 decade ago
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    Let v be the speed of the boat, c be the speed of the current.

    Downstream (in the same direction): c + v = 10/70 = 1/7 miles/min.

    Upstream (opposite directions): 10/(c - v) = 2 hrs = 120 min.

    c - v = 10/120 = 1/12 miles/min

    Summing both equations: 2c = 1/7 + 1/12 = 19/84

    c = 19/168 miles/min = 0.113 miles/min = 6.79 miles/hr

    v = 19/168 - 1/12 = 5/168 miles/min = 0.0298 miles/min = 1.79 miles/hr

  • 1 decade ago

    down stream(velocity of boat & water in same direction)

    v+x=s/t; v is velocity of boat,x is of water,s is distance,t s time...

    v+x=10/1.0167=8.57miles/hr

    up stream

    v-x=10/2=5miles/hr

    solving those two equations v=6.785miles/hr

    x=1.785miles/hr

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