44. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. find the speed of the man in still water and the speed of the current?

A. 3 km/hr B. 8 km/hr C. 5 km/hr D. 10 km/hr

Answer Answer: Option A Explanation: Let rate upstream =x km/hr and rate downstream = Y km/hr
Then 40/x+55/y = 13........(1) and 30/x+44/y = 10
Multiplying (2) by 4 and (1) by 3 and subtracting, we get 11/y =1
substituting y = 11 in (1) we get : x=5
Rate in still water = 1/2 (11+5) km/ph = 8 km/ph
Rate of current = 1/2 (11-5) km/ph = 3 km/ph

45. In a stream running at 2 km/hr. a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water?

A. 22 km/hr B. 30 km/hr C. 35 km/hr D. 40 km/hr

Answer Answer: Option A Explanation: Let the speed of the motorboat in still water be x km/hr. then,
speed downstream = (x+2) km/hr ; speed upstream = (x-2) km/hr.
Therefore 6/x+2 + 6/ x-2 = 33/60 <=> 11x^2- 240x-44=0 <=> 11x^2 - 242x+2x - 44 =0
<=> (x-22) (11x+2) =0 <=> x=22.
Hence, speed of motorboat in still water = 22 km/hr.