Question

(ii) A boat take 6 hours to travel 36 km
downstream and 24 km upstream. It takes 9
hours to travel 48 km downstream and 40 km
upstream. Find the speed of the stream and
that of boat in still water.​

Answer 1

Answer:

Total Time = Upstream distance/upstream speed + Downstream dist/downstream speed  

Let speed of boat=x

Let speed of stream=y

Upstream speed = speed of boat - speed of stream = x - y  

Down stream speed = speed of boat + speed of stream = x + y

Given 36/x+y + 24/x-y = 6 hours...... (i)

48/x+y + 40/x-y = 9 hours.......(ii)

Multiply eq.(i) by '5' and eq.(ii) by '3'

180/x+y + 120/x-y = 30.....(iii)

144/x+y + 120/x-y = 27.....(iv)

Subtract above equations:

36/x+y = 3

x+y = 12.....(a)

(a) in (iv)

144/12 + 120/x-y = 27

12 + 120/x-y = 27

120/x-y = 15

x-y = 8

x+y = 12

Adding both:

2x = 20

x=10

10+y = 12

y=2

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