Question

A motor boat whose speed is still in water is 16 km per hour takes 2 hours more to go 60 km upstream then to return to the same spot.find the speed of the stream

Answer 1

Answer:

The speed of the stream = 6 km/hr

Step-by-step explanation:

Given:

Speed of boat in still water = 18 km/hr

Let speed of the stream = s

Speed of boat upstream = Speed of boat in still water - speed of stream

Speed of boat upstream = 18 − s

Speed of boat downstream = Speed of boat in still water + speed of stream

Speed of boat downstream = 18 + s

Time taken for upstream = Time taken to cover downstream + 1

$D_u / S_u = D_d / S_d + 1$

Here,

• $D_u$ = Distance upstream

• $S_u$ = Speed upstream

• $D_d$ = Distance downstream

• $S_d$ = Speed downstream

∴ 24/(18-s) = 24/(18+s) + 1

⇒ 24(18+s) = 24(18-s) + (18-s)(18+s)

⇒ s² + 48s - 324 = 0

⇒ s² + 54s - 6s - 324 = 0

⇒ (s+54)(s-6) = 0

⇒ s = 6 , -54

⇒ s  ≠ −54 ∵ Speed of steam cannot be negative.

∴ s = 6 km/hr