Respuesta :
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.
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
[tex]Time = \frac{Distance}{speed}[/tex]
As given
A boat travels 8 miles upstream in the same time it takes to travel 16 miles downstream.
First case for the upstream
[tex]Time = \frac{8}{u - 4}[/tex]
Second case for the downstream
[tex]Time = \frac{16}{4 + u}[/tex]
now compare the equations
[tex]\frac{8}{u - 4} = \frac{16}{u + 4}[/tex]
simplify the equation
8( u +4 ) = 16 (u -4)
8u +32 = 16u - 64
8u = 96
[tex]u = \frac{96}{8}[/tex]
u = 12 mph is the speed of the boat in still water .
Hence proved
