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

Question

A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48 minutes longer

to cover the same distance against the current. Find the speed of the boat in still water and the

speed of the current.

Accepted Answer

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

And the speed of the current = y km/hr

Speed of the boat in the direction of current = (x + y) km/hr

Speed of the boat against the current = (x - y) km/hr

We know, distance = speed x time

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

44 = (x + y) x 4

x + y = 44/4

x + y = 11 … (i)

And,

x – y = 5 … (ii)

Now, adding equations (i) and (ii) we have

x + y = 11

x – y = 5

2x = 16

x = 16/2

x = 8

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

8 + y = 11

y = 11 – 8

y = 3

Therefore, the speed of the boat in still water = 8 km/hr and speed of the current = 3 km/hr.

Question 39