A boat can go 10 km upstream and 11 km downstream in a total time of 52 minutes. If the speed of the stream is 5 km/h, then what is the speed (in km/h) of the boat when going downstream?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 30.
The boat can go 10 km upstream and 11 km downstream in a total time of 52 minutes.
Speed of the stream = 5 km/h
Time = Distance/speed
Upstream speed = u - v (here, u = speed of the object, v = speed of the stream)
Downstream speed = u + v
Let the speed of the boat be x km/h;
According to the question:⇒
[10/(x - 5)] + 11/(x + 5) = 52/60
⇒ [(10x + 50 + 11x - 5)/(x - 5)(x + 5)] = 13/15
⇒ (21x - 5)/(x2 - 25) = 13/15
⇒ 315x - 75 = 13x2 - 325
⇒ 13x2 - 325 + 75 - 315x = 0
⇒ 13x2 - 315x - 250 = 0
⇒ 13x2 - 325x + 10x - 250 = 0
⇒ 13x(x - 25) + 10(x - 25) = 0
⇒ (x - 25)(13x + 10) = 0
⇒ x = 25 or - (10/13)
Since speed cannot be negative so x = 25
Speed of the boat = 25 km/h
So,
Downstream speed = 25 + 5 = 30 km/h