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

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.

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

As given

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

First case for the upstream

Second case for the downstream

now compare the equations

simplify the equation

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

8u +32 = 16u - 64

8u = 96

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

Hence proved

50.6

step-by-step explanation: