Multiple choice

A man goes from city A to city B situated 60 kms apart by a boat. His onward journey was with the stream while the return journey was an upstream journey. It took him four and half hours to complete the round trip. If the speed of the stream is 10 km/hr. How long did it take him to complete the onward journey?

  1. 3 hours

  2. 3.5 hours

  3. 2.25 hours

  4. 1.5 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let b be boat speed, s=10. Downstream speed = b+10, Upstream = b-10. 60/(b+10) + 60/(b-10) = 4.5. 60(b-10+b+10) / (b^2-100) = 4.5. 120b / (b^2-100) = 4.5. 120b = 4.5b^2 - 450. 4.5b^2 - 120b - 450 = 0. Divide by 1.5: 3b^2 - 80b - 300 = 0. (3b+10)(b-30) = 0. b = 30. Onward journey (downstream) = 60 / (30+10) = 60/40 = 1.5 hours.

AI explanation

Let the boat's speed in still water be x km/hr; the downstream speed is x + 10 and the upstream speed is x - 10. The total time for the 60 km round trip is 4.5 hours, so the equation is 60 divided by (x + 10) plus 60 divided by (x - 10) equals 4.5. Solving this gives 4.5x squared minus 1200 plus 450 equals 0, so x equals 30 km/hr. The onward downstream speed is 40 km/hr, meaning the time taken to travel 60 km downstream is 60 divided by 40, which is 1.5 hours.

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