Question

A boat covers 24 km upstream and 36 km downstream in 6 hrs while it covers 36 km upstream and 24 km downstream in 6.5 hrs. The velocity of the current is: 

a) 1 km ph 

b)1.5 km ph 

c) 2 km ph 

d) 2.5 km ph

Answer 1

Correct option: c) 2 km ph

Explanation;

Let rate upstream= x kmph and rate downstream= y kmph eqn1 :(24/x)+(36/y) =36 and eqn 2: (36/x)+(24/y) =13/2

Adding eqns 1 & 2 we get (1/x)+(1/y) =5/24(eqn 3)

Subtracting eqns 1 &2 we get (1/x)-(1/y) =1/24(eqn 4)

Adding eqns 3 & 4 we get x=8 kmph therefore y=12 kmph

Rate of current =1/2*(12-8) =2 kmph