Question

a person can row a boat at 10 km per hour in still water he takes two and half hours to row from a to b and back if the distance between a and b is 12 km then the speed of stream is

Answer 1

Given:

Speed of boat = 10 km per hour

The total time taken is = 2$\frac{1}{2}$ hours = 5/2 hours

Distance from A to B = 12 km

To find:

Speed of the stream.

Solution:

Let us take speed of the stream as ' y '

The formula for upstream speed and downstream speed is given by

• Upstream speed (U) = speed of boat - speed of stream

⇒ U  = (10 - y)  km per hour                 ( Equation 1)                                        

                             

• Downstream speed ( V) = speed of boat + speed of stream

⇒ V = (10 + y) km per hour                 ( Equation 2)

As we know that, Speed = Distance / time

total time ' T ' = t₁ + t₂

$\frac{5}{2}$ = t₁ + t₂

Putting equations 1 and 2 in the formula for the speed, we can get the equations in terms of time.

t₁ =  $\frac{12}{10+y}$

t₂ = $\frac{12}{10-y}$

Therefore,

$\frac{12}{10+y}$ + $\frac{12}{10-y}$ = $\frac{5}{2}$

On solving the above equation, we get

y = 2 km per hour

The speed of the stream is 2 km per hour.