Question

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

• A. 4, 7
• B. 7, 8
• C. 3,2
• D. 6, 3

Answer 1

The correct option is A 4, 7

Let, us assume that the speed of boat in still water is x km/hr and speed of stream is y km/hr
So, the speed of boat upstream will be (x - y) km/hr
Similarly the speed of boat downstream will be $(x+y)$ km/hr
We mknow that,
time $=\frac{\text{distance}}{\text{speed}}$
Using the above formula we can form the equation in two variables.
Taking the first case
$\Rightarrow \frac{30}{(x-y)}+\frac{44}{(x+y)}=14$
Taking up the second case
$\Rightarrow \frac{60}{(x-y)}+\frac{55}{(x+y)}=25$
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 we get.

$\Rightarrow 30u+44v=14$
$\Rightarrow 60u+55v=25$
We can solve the above two equations using elimination method.
$\Rightarrow 60u+88v=28$
$\Rightarrow 60u+55v=25$
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
$\Rightarrow x-y=3$
$\Rightarrow x+y=11$
Solving the above two equations we get $x=7,y=4$
So, the speed of stream is 4 km/hr and the speed of boat in still water is 7 km/hr.