Question

The speed of a stream is 4 mph. A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream. what is the speed of the boat in still water

Answer 1

Answer

Find out the speed of the boat in still water .

To proof

Let us assume that the speed of the boat in still water be u .

As given

The speed of a stream is 4 mph

hence

speed upstream = u - 4

speed downstream = u + 4

Formula

$Time = \frac{Distance}{speed}$

As given

A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream.

First case for the upstream

$Time = \frac{8}{u - 4}$

Second case for the downstream

$Time = \frac{16}{4 + u}$

now compare the equations

$\frac{8}{u - 4} = \frac{16}{u + 4}$

simplify the equation

8( u +4 ) = 16 (u -4)

8u +32 = 16u - 64

8u = 96

$u = \frac{96}{8}$

u = 12 mph is the speed of the boat in still water .

Hence proved

   

   

Answer 2

The speed of the stream = 4 mph.

Let us assume speed of the boat in still water = x mph.

Total speed upstream = (x-4) mph.

Total speed downstream = (x+4) mph.

We know,  time, speed and distance relation.

Time = Distance / Speed.

Total time taken upstream = 8 / (x-4)

Total time taken downstream = 16/(x+4).

Time taken upstream = time taken downstream.

Therefore,

8 / (x-4)  =  16/(x+4).

On cross multiplication, we get

16(x-4) = 8(x+4).

16x - 64 = 8x +32.

Adding 64 on both sides, we get

16x - 64+64 = 8x +32+64

16x = 8x + 96.

Subtracting 8x from both sides, we get

16x-8x = 8x-8x + 96.

8x = 96.

Dividing both sides by 8, we get

x = 12.

Therefore, 12 mph is the speed of the boat in still water.