Question

a boat goes 12km upstream and 40 km down stream in 8 hours .ti can go 16 km upstream and 32 km down stream in the same time. find the speed of the boat in still water and the speed of up stream

Answer 1

Let the speed of the boat in still water be x km/hr.

Let the speed of the stream be y km/hr.

So, the speed of the boat upstream = x-y

The speed of the boat downstream  = x+y

Since,
$time = \frac{distace}{time}$
Therefore,
$8 = \frac{12}{x - y} + \frac{40}{x + y}$
suppose,
$\frac{1}{x - y} = u \\ \frac{1}{x + y} = d$
So, the equations become 8 = 12u+ 40d

               and  8 = 16u + 32d

Now, solve the equations for u and d by elimination method and replace u by x-y and d by x+y.

You get, x-y = 4

     x+y = 8

Solve these equations for x and y by elimination method. So, the speed of the boat in still water is 6 km/hr. and the speed of the stream is 2 km/hr.