Jake and Paul start together to walk 10 kms. Jake walks 1.5 kmph faster than…
2025
Jake and Paul start together to walk 10 kms. Jake walks 1.5 kmph faster than Paul and arrives at his destination 1.5 hours earlier than Paul. Jake's speed is ?
- A.
6 kmph
- B.
2 kmph
- C.
4 kmph
- D.
8 kmph
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Correct answer: C
Answer: 4 kmph
Let Jake's speed be x km/h and Paul's speed be x - 1.5 km/h.
The difference in their travel times for 10 km is: 10/(x - 1.5) - 10/x = 1.5.
Combine terms: (10x - 10(x - 1.5)) / (x(x - 1.5)) = 1.5, so 15 / (x(x - 1.5)) = 1.5.
Thus x(x - 1.5) = 10, which gives x^2 - 1.5x - 10 = 0.
Solve the quadratic: x = [1.5 ± sqrt(1.5^2 + 40)] / 2 = [1.5 ± 6.5] / 2.
The positive root is x = (1.5 + 6.5)/2 = 4 km/h (negative root is discarded).
Check: Jake's time = 10/4 = 2.5 h; Paul's time = 10/2.5 = 4 h; difference = 1.5 h. Hence Jake's speed is 4 km/h.