Problems on Simultaneous Linear Equations | Problems on Simultaneous Linear Equations Exercise 6

Question

A boat takes 2 hours to go 40 km down the stream and it returns in 4 hours. Find the speed of

the boat in still water and the speed of the stream.

Accepted Answer

Let’s assume the speed of the boat in still water be x km/hr

And the speed of the stream = y km/hr

So, the speed of the boat in downstream = (x + y) km/hr

The speed of the boat in upstream = (x - y) km/hr

We know,

Distance = Speed x time

Now, according to the given conditions in the problem, we have

40 = (x + y) × 2

x + y = 20 … (i)

And,

40 = (x - y) × 4

x – y = 10 … (ii)

Adding (i) and (ii), we have

x + y = 20

x – y = 10

2x = 30

x = 15

On substituting the value of x in equation (i), we have

15 + y = 20

y = 20 – 15

y = 5

Therefore, speed of the boat in still water = 15 km/hr and speed of the stream = 5 km/hr.

Question 38