Question

Search boat covers 24 km upstream and 36 km downstream in 6 hours. And it goes 36km upsteam and 24km downstream in 61/2 hrs find the speed of boat

Answer 1

Let rate upstream = x km/h and rate downstream = y km/h
Then,(24/x) + (36/y) = 36 ------(i)
and (36/x) + (24/y) = 13/2 -------(ii)
Adding (i) and (ii),
60((1/x) + (1/y)) = 25/2
=> (1/x) + (1/y) = 5/24 -------(iii)
Subtracting (i) from (ii)
12((1/x) - (1/y)) = 1/2
=> (1/x) - (1/y) = 1/24 --------(iv)
Adding (iii) and (iv)
2/x = 6/24
=> x = 8
So (1/8) + (1/y) = 5/24
=> y = 12
Speed Upstream = 8 km/h and
Speed Downstream = 12 km/h
So,Velocity of Current = (1/2) * (12-8)
= 2 km/h