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Two people, John and Clara, are walking along the same road from Town Updated on: 26 Apr 2026, 11:03
Originally posted by Bunuel on 10 Feb 2026, 23:58.
Last edited by Bunuel on 26 Apr 2026, 11:03, edited 1 time in total.
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81% (02:49) correct 19% (02:40) wrong based on 77 sessions

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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

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Two people, John and Clara, are walking along the same road from Town Updated on: 19 Feb 2026, 06:04
Originally posted by Bunuel on 19 Feb 2026, 06:00.
Last edited by Bunuel on 19 Feb 2026, 06:04, edited 1 time in total.
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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
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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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Two people, John and Clara, are walking along the same road from Town 11 Feb 2026, 00:21
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Since the time (t) is constant for both walkers until they meet, the distance they travel is directly proportional to their speeds.

Ratio of Speeds (John : Clara) = 3 : 4
Ratio of Distances (John : Clara) = 3 : 4
Total "parts" of distance = 3 + 4 = 7 units.

We know the total distance covered by both is 2 * 21 = 42 km.

1 unit = 42/7 = 6 km.
John’s distance (X to R) = 3 units * 6 = 18 km.

Correct Answer: D (18 km)
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Two people, John and Clara, are walking along the same road from Town 11 Feb 2026, 00:35
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X _____21-x_km__________R_____x km____ Y

Time taken by John and Clara to travel and meet at R will be same.
T_J = (21-x)/3
T_C = (21 +x)/4

T_J = T_C, solving this gives x =3 km.
Thus distance XR will be 21-3 = 18km

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

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Two people, John and Clara, are walking along the same road from Town 11 Feb 2026, 01:30
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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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