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Key Insight: Both John and Clara walk for the same amount of time until they meet. Clara just covers more distance because she's faster and has to reach Town Y first, then walk back.

Setting Up the Problem:
Let's say they meet after t hours.

John's position after t hours:
John walks at 3 km/hr, so he covers 3t km from Town X.

Clara's position after t hours:
Clara walks at 4 km/hr, so she covers 4t km total.
But here's the twist - Clara first walks 21 km to reach Town Y, then turns around and walks back toward X.

So Clara's distance from X = 21 - (distance she walked back)
= 21 - (4t - 21)
= 42 - 4t km

At the meeting point R, their positions are equal:
3t = 42 - 4t
7t = 42
t = 6 hours

Distance from X to R:
= 3t = 3 × 6 = 18 km

Quick Verification:
- John walks 18 km in 6 hours at 3 km/hr ✓
- Clara walks 4 × 6 = 24 km total (21 km to Y + 3 km back), ending up 18 km from X ✓

Answer: D (18 km)
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Bunuel
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
GMAT Club Official Solution:

Clara reaches Town Y in 21/4 hours, so by then John has walked 3 * 21/4 = 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 - 63/4 = 21/4 km, so time to meet is (21/4)/7 = 3/4 hour.

In 3/4 hour, John walks 3 * 3/4 = 9/4 km more, so distance X to R is 63/4 + 9/4 = 18 km.

Answer: D.
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