Question
Download Solution PDFA boat takes 3 hours more to travel 300 km upstream than to travel 280 km downstream. If the speed of the current is 14.28% of the speed of the boat, what is the speed of the boat in still water?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Upstream distance = 300 km
Downstream distance = 280 km
Speed of current = 14.28% of boat's speed in still water
Time difference = 3 hours (Upstream takes 3 hours more)
Let the speed of the boat in still water be x km/h:
Speed of current = 14.28% of x = (14.28 / 100) × x = x/7 km/h
Calculate upstream and downstream speeds:
Upstream speed = x - x/7 = 6x/7 km/h
Downstream speed = x + x/7 = 8x/7 km/h
Time upstream = Distance ÷ Speed = 300 ÷ (6x/7)
Time downstream = 280 ÷ (8x/7)
According to the problem:
Time upstream - Time downstream = 3
⇒ (300 / 6x/7) - (280 / 8x/7) = 3
⇒ (2100 / 6x) - (1960 / 8x) = 3
Multiply both sides by x:
⇒ (2100 / 6) - (1960 / 8) = 3x
2100 / 6 = 350
1960 / 8 = 245
⇒ 350 - 245 = 3x
⇒ 105 = 3x
⇒ x = 105 ÷ 3 = 35 km/h
Thus, the correct answer is 35 km/h.
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