Question

a motor boat whose speed in still water is 18 km/h , takes one hour more to go 24 km upstream than to return downstream to the same spot . find the speed of the stream.

Answer 1

Heyya!

Given, speed of the boat in still water = 18 km/hr.

Let the speed of the stream be x km/hr.

Speed of the boat upstream = Speed of boat in still water – Speed of the stream

∴ Speed of the boat upstream = ( 18 – x ) km/hr

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

∴ Speed of the boat downstream = ( 18 + x ) km/hr

Time of upstream journey = Time for downstream journey + 1 hr

⇒ 48x = 324 – x2 

⇒ x2 + 48x – 324 = 0

∴ x = 6  (Speed of the stream cannot be negative)

Thus, the speed of stream is 6 km/hr.

Hope it helps!☺

Answer 2

Let the speed of the stream be x km/h

Speed of the motor boat = 18 km/h

Upstream :

Speed = (18 - x) km/h

Distance = 24 km

Time = Distance ÷ Speed

Time = 24 / (18 - x)

Downstream :

Speed = (18 + x) km/h

Distance = 24 km

Time = Distance ÷ Speed

Time = 24 / (18 + x)

Solve x:

The difference in time is 1 hour

24/(18 - x) - 24/(18 + x) = 1

24(18 + x) - 24(18 - x) =  (18 - x)(18 + x)

432 + 24x - 432 + 24x  = (18)² - x²

48x = 324 - x²

x²  + 48x - 324 = 0

(x - 6) ( x + 54) = 0

x = 6 or x = 54 ( rejected, speed cannot be negative)

x = 6

Answer: The speed of the stream is 6 km/h