Question
Download Solution PDFA boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7 : 6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Upstream time = 51 minutes = 51 ÷ 60 = 0.85 hours
Upstream distance = 10.2 km
Speed ratio (boat : stream) = 7 : 6
Formula used:
Speed = Distance ÷ Time
Upstream speed = Boat speed − Stream speed
Downstream speed = Boat speed + Stream speed
Calculations:
⇒ Upstream speed = 10.2 ÷ 0.85 = 12 km/hr
Let boat speed = 7x, stream speed = 6x ⇒ upstream = 7x − 6x = x
⇒ x = 12 ⇒ boat speed = 7x = 84 km/hr, stream speed = 6x = 72 km/hr
⇒ Downstream speed = 84 + 72 = 156 km/hr
⇒ Time for 17.7 km upstream = 17.7 ÷ 12 = 1.475 hours
⇒ Time for 66.3 km downstream = 66.3 ÷ 156 = 0.425 hours
⇒ Total time = 1.475 + 0.425 = 1.9 hours
∴ Total time taken = 1.9 hours
Last updated on Jul 19, 2025
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