Question

A boat travels upstream from Q to P and downstream from P to Q in 3hrs. if the distance between P to Q is 4km and the speed of the stream is 1kmph, then what is the speed of the boat in still water?

Answer 1

Let X be the speed of boat then
upstream speed of boat is (x-1)kph
downstream speed of boat is (x+1)kph
by condition,
4/(x-1)+4/(x+1)=3
4x+4+4x-4=3 (x×x-1)
8x=3x×x-3
=>x=3kph (using splitting middle term )
may help u

Answer 2

The speed of the boat in still water is 3 kmph.

• Given:

The time taken by the boat upstream from Q to P and downstream from P to Q is 3hrs.

Now the distance between P and Q is 4 km.

Speed of the stream is 1 kmph.

• Let the speed of the boat in still water be x kmph.

• Now the speed of the boat downwards will be (x+1)kmph and the speed of the boat upstream will be (x-1) kmph.

• Now, the time taken = $|frac{Distance}{Speed}$.

• Total time = Time taken Upstream + Time taken Downstream

3 = $|frac{4}{x-1}$ + $|frac{4}{x+1}$

3(x²-1) = 4x-4 + 4x+4

3x²-8x-3 = 0

3x²-9x+x-3 =0

3x(x-3)+1(x-3) =0

(3x + 1)(x-3)=0

x = 3 or x= -1/3

But speed of the boat cannot be negative.

∴ x = 3 kmph

• Speed of the boat in still water is 3 kmph.