Question

The time taken to travel 30km upstream and 44 km downstream is 14 hr. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km, then total time taken is 11hr more than earlier. Find the speed of the stream and speed of the boat.

• A. 4,7
• B. 7,8
• C. 3,2
• D. 6,3

Answer 1

The correct option is A

4,7

Lets assume that the speed of boat in still water is x $\frac{km}{hr}$ and speed of stream is y$\frac{km}{hr}$.

So the speed of boat in upstream will be (x-y)$\frac{km}{hr}$.

Similarly the speed of boat in downstream will be (x+y)$\frac{km}{hr}$.

We know time = ( $\frac{distance}{speed}$)

Using the above formula we can form the equation in two variables.

Taking the first case

$\frac{30}{x-y}$ + $\frac{44}{x+y}$ = 14

Taking up the second case

$\frac{60}{x-y}$ + $\frac{55}{x+y}$ = 25

Now we have the equation in two variables but the equations are not linear

So we will assume $\frac{1}{x-y}$ as u and $\frac{1}{x+y}$ as v

So substituting u and v in the above two equations.

30u + 44v = 14

60u + 55v = 25

We can solve the above two equations using elimination method.

60u + 88v = 28

60u + 55v = 25

Subtracting the above two equations we get v = $\frac{1}{11}$

Substituting v in any of above two equation we get u = $\frac{1}{3}$

Now as we have assumed

$\frac{1}{x-y}$ = u and $\frac{1}{x+y}$ = v

Putting the values of u and v

We get another linear equation in x,y

x - y = 3

x + y = 11

Solving the above two equations we get x = 7, y = 4

So speed of boat in still water is 7 $\frac{km}{hr}$ and speed of stream is 4 $\frac{km}{hr}$.