Question

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

• A. 4 km/hr
• B. 7 km/hr
• C. 3 km/hr
• D. 6 km/hr

Answer 1

The correct option is A

4 km/hr

Let's assume that the speed of the boat in still water is x km/hr and speed of the stream is y km/hr.

So, the speed of the boat in upstream will be (x-y) km/hr.

Similarly, the speed of the boat downstream will be (x+y) km/hr.
We know $\text{time}=\left(\frac{\text{distance}}{\text{speed}}\right)$.

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

Taking the first case,

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

Taking the second case,

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

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

So, we will assume $\frac{1}{\text{x - y}}=\text{u}$ and $\frac{1}{\text{x + y}}=\text{v}$.

So on substituting $\text{u}$ and $\text{v}$ in the above two equations, we get

$30\text{u}+44\text{v}=14$ ...(1)

$60\text{u}+55\text{v}=25$ ...(2)

We can solve the above two equations using the elimination method.

$60\text{u}+88\text{v}=28$ ...(3)
(by multiplying equation (1) by 2)

On subtracting equation (2) from (3), we get $\text{v}=\frac{1}{11}$

On substituting $\text{v}$ in equation (2) we get $\text{u}=\frac{1}{3}$

Now as we have assumed

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

On substituting the values of $\text{u}$ and $\text{v}$,

we get a pair of linear equations in $\text{x and y}$

$\text{x - y}=3$...(4)

$\text{x + y}=11$...(5)

On adding (5) from (4), we have

$2x=14$

$x=7$

On subsituting the value of x in $x-y=3$, we get y = 4.

So, the speed of the boat in still water is 7 km/hr and the speed of the stream is 4 km/hr.