Question

The wind is moving in the direction of upstream at 4 km/hr and water is flowing at 2 km/hr. A boat takes 17 hours to cover 60 km in upstream and 96 km in downstream. What is the speed of the boat in still water in wind direction?
1. 8 km/hr
2. 10 km/hr
3. 14 km/hr
4. 15 km/hr

Answer 1

Correct Answer - Option 3 : 14 km/hr

Given:

Speed of wind = 4 km/hr

Speed of stream = 2 km/hr

Time taken by boat to cover 60 km/hr in upstream and 96 km/hr in downstream = 17 hours.

Formula used:

Boat's speed in upstream = Speed of boat in still water + Speed of wind - Speed of stream

Boat's speed in downstream = Speed of boat in still water - Speed of wind + Speed of stream

Time = Distance/Speed

Calculations:

Let the speed of boat in still water be x km/hr.

Boat's speed in upstream = Speed of boat in still water + Speed of wind - Speed of stream

⇒ x + 4 - 2

⇒ x + 2

Boat's speed in downstream = Speed of boat in still water - Speed of wind + Speed of stream

⇒ x - 4 + 2

⇒ x - 2

According to question,

Time = Distance/Speed

⇒ 60/(x + 2) + 96/(x - 2) = 17

⇒ 60(x - 2) + 96(x + 2) = 17x² - 68

⇒ 17x²- 156x - 140 = 0

⇒ x = 10 or -14/17

As speed cannot be in negative, 

⇒ x = 10 km/hr

The speed of the boat in still water in wind direction = (x +  4)

⇒ (x + 4) = 14 km/hr

∴ The speed of the boat in still water in wind direction is 14 km/hr.