A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.
A) 12 km/hr, 3 km/hr
B) 9 km/hr, 3 km/hr
C) 8 km/hr, 2 km/hr
D) 9 km/hr, 6 km/hr
Answers
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Answer:
B) 9 km/hr, 3 km/hr
Step-by-step explanation:
Let say Boat Speed = B km/Hr
River Speed = R km/Hr
Downstream speed = B + R k/Hr
Upstream speed = B - R km/Hr
Time taken for downstream = 28/(B-R)
Time taken for upstream = 28/(B+R)
time taken for upstream is double of time taken for downstream
28/(B-R) = 2 * 28/(B+R)
=> B + R = 2B - 2R
=> B = 3R
if R were 2R
then downstram speed = B + 2R = 3R + 2R = 5R km/Hr
upstram speed = B - 2R = 3R - 2R = R km/Hr
total time = 28/5R + 28/R = 672/60
=> 28 * 12 + 28 * 60 = 672R
=> 12 + 60 = 24R
=> 1 + 5 = 2R
=> R = 3
Speed of River = 3 km/Hr
Speed of Boat = 3R = 9 km/Hr
option B is correct Answer
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