A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the Boat in still water and the speed of the stream.

Matching exercise

    
Match the items on the right to the items on the left.
STEP 1
STEP 2
STEP 3
STEP 4
STEP 5
Speed = distance/time


Let the speed of boat be ‘a’ and speed of stream be ‘b’


Relative speed of boat going upstream = a – b


Relative speed of boat going downstream = a + b
Given, boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time Q10.png
Equating (1) and (2), we get


⇒ 8/(a + b) = 4/(a – b)


⇒ a = 3b

Substitute value of a in eq1


⇒ 12/2b + 40/4b = 8


⇒ 16/b = 8

⇒ b = 2 km/hr


Thus, a = 6 km/hr.