## Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream.

Question

Q3) A boat takes 9 hours to travel 30 km upstream and 40 km downstream but it takes 12 hours to travel 42 km upstream and 50 km downstream. Find the speed of the boat in still water and the speed of the stream

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2 weeks 2021-11-19T16:31:21+00:00 2 Answers 0 views 0

2. ## SOLUTION ::

Let the speed of the boat in still water = x km/h

The speed of the stream = y km/h

We know that

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

Upstream speed

= speed of boat – speed of stream

= x – y

Down stream speed = x + y

BY THE GIVEN CONDITION

30/x-y + 40/x+y = 9 …………. (i)

42/x-y + 50/x+y = 12 ………….(ii)

Multiplying eq.(i) by 5 & eq.(ii) by 4

150/x-y + 200/x+y = 45 ……(iii)

168/x-y + 200/x+y = 48 ……(iv)

Now (iii) – (iv) gives

-18/x-y = – 3

x-y = 6 …..(v)

Substituting (v) in (iii)

150/x-y + 200/x+y = 45

150/6 + 200/x+y = 45

200/x+y = 20

x + y = 10……..(vi)

Adding (v) & (vi) We get

2x = 16

x = 8

8+y = 10

y= 2

Hence speed of boat = 8 km/h

Speed of stream = 2 km/h