Question

When a boat goea upstream for a distance of 24 km and downstream for 24 km with a speed of 18km/h,the time difference is 1 hour.Find the speed of the stream?

please answer this question with all the steps clearly with reason for each and everything

Answer 1

Answer : Speed of stream= 6 km/hr

Sol:

Let the speed of the stream be x km/hr

Speed of the boat in still water = 18 km/hr

Speed of the boat in upstream = (18 - x) km/hr

Speed of the boat in downstram = (18 + x) km/hr

Distance between the places is 24 km.

Time to travel in upstream = d / (18 - x) hr

Time to travel in downstream = d / (18 + x) hr

Difference between timings = 1 hr

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

⇒ 24 [1 / (18 - x)] - [1 / (18 + x)] = 1

⇒ [1 / (18 - x)] - [1 / (18 + x)] = 1/24

⇒ (18 + x - 18 + x) / (324 - x²) = 1/24

⇒ (2x) / (324 - x²) = 1/24

⇒ 324 - x² = 48x

⇒ x² - 48x + 324 = 0

⇒ (x + 54)(x - 6) = 0

x = - 54 or 6

Speed of the stream can not be negative.

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