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26 Apr 2026, 11:03
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Two people, John and Clara, are walking along the same road from Town X to Town Y, a distance of 21 kilometers. John walks at 3 kilometers per hour, while Clara walks at 4 kilometers per hour. Clara reaches Town Y, immediately turns back along the same road, and meets John at point R while John continues walking toward Town Y. What is the distance from Town X to R?
A. 12 km
B. 15 km
C. 16.8 km
D. 18 km
E. 20 km
A. 12 km
B. 15 km
C. 16.8 km
D. 18 km
E. 20 km
26 Apr 2026, 11:03
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Official Solution:
Two people, John and Clara, are walking along the same road from Town X to Town Y, a distance of 21 kilometers. John walks at 3 kilometers per hour, while Clara walks at 4 kilometers per hour. Clara reaches Town Y, immediately turns back along the same road, and meets John at point R while John continues walking toward Town Y. What is the distance from Town X to R?
A. 12 km
B. 15 km
C. 16.8 km
D. 18 km
E. 20 km
Clara reaches Town Y in \(\frac{21}{4}\) hours, so by then John has walked \(3 * \frac{21}{4} = \frac{63}{4}\) km.
At that moment Clara turns back, and they move toward each other, so the gap closes at \(4 + 3 = 7\) km/h.
The gap is \(21 - \frac{63}{4} = \frac{21}{4}\) km, so time to meet is \(\frac{\frac{21}{4}}{7} = \frac{3}{4}\) hour.
In \(\frac{3}{4}\) hour, John walks \(3 * \frac{3}{4} = \frac{9}{4}\) km more, so distance X to R is \(\frac{63}{4} + \frac{9}{4} = 18\) km.
Answer: D
Two people, John and Clara, are walking along the same road from Town X to Town Y, a distance of 21 kilometers. John walks at 3 kilometers per hour, while Clara walks at 4 kilometers per hour. Clara reaches Town Y, immediately turns back along the same road, and meets John at point R while John continues walking toward Town Y. What is the distance from Town X to R?
A. 12 km
B. 15 km
C. 16.8 km
D. 18 km
E. 20 km
Clara reaches Town Y in \(\frac{21}{4}\) hours, so by then John has walked \(3 * \frac{21}{4} = \frac{63}{4}\) km.
At that moment Clara turns back, and they move toward each other, so the gap closes at \(4 + 3 = 7\) km/h.
The gap is \(21 - \frac{63}{4} = \frac{21}{4}\) km, so time to meet is \(\frac{\frac{21}{4}}{7} = \frac{3}{4}\) hour.
In \(\frac{3}{4}\) hour, John walks \(3 * \frac{3}{4} = \frac{9}{4}\) km more, so distance X to R is \(\frac{63}{4} + \frac{9}{4} = 18\) km.
Answer: D
