A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 39 km upstream?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3 h 40 m.
Given:
Speed of motorboat in still water = 20 km/h
Concept USed:
Time = Distance/speed
Explanation:
Let the stream of speed be 'x'
⇒ (1/2) = 24/(20 - x) - 24/(20 + x)
⇒ (1/2) = 24(2x/(400 - x2))
⇒ (1/2) = 48x/(400 - x2)
⇒ 400 - x2 = 96x
⇒ x2 + 96x - 400 = 0
⇒ x2 - 4x + 100x - 400 = 0
⇒ x(x - 4) + 100(x - 4) = 0
⇒ (x - 4)(x + 100) = 0
⇒ x = 4
Now, speed of the boat in still water is increased by 2 kn/hr:
New upstream speed = 22 - 4 = 18 km/h
New downstream speed = 22 + 4 = 26 km/h
Time taken = 39/18 + 39/26
⇒ 13/6 + 3/2 = (13 + 9)/6
⇒ 22/6 or 11/3 ⇒ 3 hours 40 minutes
Hence, it take 3 h 40 min to go 39 km downstream and 39 km upstream.