A boat moves at 15 kilometres per hour in still water. The stream speed is x. It takes 4 hours to go 36 kilometres downstream and 24 kilometres upstream. What is x?
Answer and explanation
Correct answer: 3
For a boat and stream, downstream speed is 15 + x and upstream speed is 15 − x. Therefore the total-time equation is 36/(15 + x) + 24/(15 − x) = 4, with 0 < x < 15. Testing the proposed value x = 3 gives downstream speed 18 and upstream speed 12. The corresponding times are 36/18 = 2 hours and 24/12 = 2 hours, whose sum is 4 hours. Thus x = 3 satisfies the original condition. For completeness, clearing denominators produces a quadratic whose admissible root is 3; any root violating x < 15 would be physically invalid. Options 2, 4, and 5 do not make the two travel times add to exactly four hours.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For a boat and stream, downstream speed is 15 + x and upstream speed is 15 − x. Therefore the total-time equation is 36/(15 + x) + 24/(15 − x) = 4, with 0 < x < 15. Testing the proposed value x = 3 gives downstream speed 18 and upstream speed 12. The corresponding times are 36/18 = 2 hours and 24/12 = 2 hours, whose sum is 4 hours. Thus x = 3 satisfies the original condition. For completeness, clearing denominators produces a quadratic whose admissible root is 3; any root violating x < 15 would be physically invalid. Options 2, 4, and 5 do not make the two travel times add to exactly four hours.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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