Question

There is a race between two boats –A and B. Both boats have to travel a distance of 320 km downstream or upstream, irrespective of the other boat. Speed of A is double that of boat B and maximum headstart it can give to B is 70 hrs and maximum headstart boat B can give to A is 4 hrs. What is the speed of boat A?

Answer 1

Given:

Distance of the boat = 320km

Speed of A = Double of B

Headstart A can give to B = 70 hrs

Headstart b can give to A = 4 hrs

To Find:

Speed of boat A

Solution:

Let the speed of the river stream be = y

Let the speed of B = x

Let the speed of A = 2x

Case 1 - When A is moving downstream and B is moving upstream

= 320/ (2x+y) + 70 = 320/x - y --- eq 1

Case 2 - When B is moving downstream and A is moving upstream

= 320/ (x+y) + 4 = 320/2x - y --- eq 2

Solving equations 1 and 2

x = 12 and y = 8

Thus,  

Speed of A = 2x

= 2 x 12 = 24

Answer: The speed of boat A is 24km/hr