I need math help please! ?

A small fishing boat heads to a point 24 miles downriver and then returns. The rivers current moved at 3 miles per hour. If the trip up and back takes 6 hours and the boat keeps a constant speed relative to the water, what is the speed of the boat? ( hint: if v is the speed of the boat, then it’s speed downriver is (v+3) miles per hour and it’s speed upriver is (v-3) miles per hour. ) 

1 Answer

  • Vaman
    Lv 7
    4 months ago
    Favorite Answer

    Distance travelled is 48 miles.

    Let v be the speed of the boat and r is the speed ot the river.

    Time to go t1= 24/(x+r). Time to come back t2= 24/(x-r). t1+t2= 6.

    6= 24/(x+r)+24/(x-r), (x^2-r^2)=4(x-r)+4x+r=8x.

    x^2 -8x = r^2=9.

    Add 16. You will have

    x^2-8x+16=(x-4)^2=5^2. x= 4+/-5. So select the plus sign. You get x=9.

    While going down the river the time taken = 24/12=2 hours, while coming up 24/6=4 hours.

    You get only one condition. You need the second condition.

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