A man goes from city A to city B situated 60 km apart by a boat . His onward…
2023
A man goes from city A to city B situated 60 km 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 he onward journey ?
- A.
3 hours
- B.
3.5 hours
- C.
2.25 hours
- D.
1.5 hours
Attempted by 3 students.
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Correct answer: D
Answer: 1.5 hours
Let the boat's speed in still water be x km/h. Stream speed = 10 km/h, so downstream speed = x + 10 and upstream speed = x - 10.
Set up the time equation for the round trip: 60/(x + 10) + 60/(x - 10) = 9/2 (since total time = 4.5 hours).
Multiply both sides by (x^2 - 100) and simplify: 60(x - 10) + 60(x + 10) = (9/2)(x^2 - 100) ⇒ 120x = (9/2)(x^2 - 100).
Clear denominators and rearrange to get a quadratic: 240x = 9(x^2 - 100) ⇒ 9x^2 - 240x - 900 = 0 ⇒ divide by 3 ⇒ 3x^2 - 80x - 300 = 0.
Solve the quadratic: discriminant = 80^2 + 4*3*300 = 6400 + 3600 = 10000, sqrt = 100. So x = (80 ± 100)/6. The positive solution is x = (80 + 100)/6 = 30 km/h.
Downstream (onward) speed = x + 10 = 40 km/h, so onward time = 60/40 = 1.5 hours.