Question
The ratio of the boat's speed in
still water to the speed of the stream is 10:2. The boat takes time in the ratio 11:15 to travel (d − 70) km upstream and (d + 30) km downstream. Find the approximate value of 'd'.Solution
Let boat speed = 10x, stream speed = 2x Upstream speed = 8x, Downstream speed = 12x Upstream time = (d − 70) / 8x Downstream time = (d + 30) / 12x Given time ratio: (d − 70)/8x ÷ (d + 30)/12x = 11/15 ⇒ (12(d − 70)) / (8(d + 30)) = 11/15 ⇒ (3(d − 70)) / (2(d + 30)) = 11/15 Cross-multiply: 15 × 3(d − 70) = 11 × 2(d + 30) ⇒ 45d − 3150 = 22d + 660 ⇒ 23d = 3810 ⇒ d = 165.65 km or aprox 165 km
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