A boatman can row a boat in still water at a speed of 9 km/h. He can also row 44 km downstream and 35 km upstream in 9 hours. How much time (in hours) will he take to row 33 km downstream and 28 km upstream ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 7.
Given:
Speed of boat in still water = 9 km/h
A boatman can also row 44 km downstream and 35 km upstream in 9 hours.
Concept used :
Distance/speed = time
Explanation:
The speed of boat in still water = 9 km/h
Let the speed of current be x km/h.
Then, speed in downstream = (9 + x) km/h
And, speed in upstream = (9 - x) km/h
According to the question ,
[44/(9 + x)] + [35/(9 - x)] = 9
⇒ 44(9 - x) + 35(9 + x) = 9(92 - x2) (By taking LCM)
⇒ 396 - 44x + 315 + 35x = 729 - 9x2
⇒ 9x2 -9x -18 = 0
⇒ x2 -x -2 = 0
⇒ x2 - 2x + x - 2 = 0
⇒ (x - 2)(x + 1) = 0
⇒ x = 2
Hence the speed of the stream = 2 km/h
Now, required time,
⇒ [33/(9 + 2)] + [28/(9 - 2)] = 3 + 4 = 7 hours.
Hence he will take 7 hours to row 33 km downstream and 28 km upstream.