X, Y and Z travel from the same place with uniform speeds 4 \text{ km/hr}, 5 \text{ km/hr} and 6 \text{ km/hr} respectively. Y starts 2 hours after X. After how much time should Z start after Y so that they both overtake X at the same time?
- A. \frac{3}{2} hours
- B. \frac{4}{3} hours ✓
- C. \frac{9}{8} hours
- D. \frac{11}{8} hours
Correct Answer: B. \frac{4}{3} hours
Explanation
Y catches X when the distance covered is equal: 4(t+2) = 5t \Rightarrow t = 8 hours. The meeting point is 40 \text{ km} away. For Z to reach 40 \text{ km} at 6 \text{ km/hr}, Z takes \frac{40}{6} = \frac{20}{3} hours. The difference in start times between Z and Y is 8 - \frac{20}{3} = \frac{4}{3} hours.
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