Question

A boat goes 44 km downstream in 4 hours and takes 4 hours 48 minutes longer in the same return journey. Find the speed of boat in still water and the speed of current.

Answer 1

Given:

• Distance downstream = 44 km
• Time downstream = 4 hours
• Time upstream = 4 hours 48 minutes longer than downstream = 4 + 4.8 = 8.8 hours

Let:

• Speed of boat in still water = (x) km/h
• Speed of current = (y) km/h

Step-wise calculation:

1. Speed downstream = x + y

2. Speed upstream = x – y

From the downstream journey:

`44/(x + y) = 4`

⇒ `x + y = 44/4`

⇒ x + y = 11   ...(Equation 1)

From upstream journey, time = 8.8 hours:

`44/(x - y) = 8.8`

⇒ `x - y = 44/8.8`

⇒ x – y = 5   ...(Equation 2)

Add Equations 1 and 2:

(x + y) + (x – y) = 11 + 5

⇒ 2x = 16

⇒ x = 8

Subtract Equation 2 from 1:

(x + y) – (x – y) = 11 – 5

⇒ 2y = 6

⇒ y = 3

Speed of boat in still water (x = 8) km/h.

Speed of current (y = 3) km/h.

Thus, the boat’s speed in still water is 8 km/h and the speed of the current is 3 km/h.