The distance between Town W and Town X was 194 km. At 05 00, Yen left Town W and cycled towards Town X. Xylia left Town W and cycled towards Town X at 05 30. Xylia's cycling speed was 2 km/h faster than Yen. At 12 00, Xylia caught up with Yen. When Xylia was 38 km from Town X, she stopped to wait for Yen. How far was Yen from Xylia when she stopped to wait for him?
Duration in which Xylia cycled for before she caught up with Yen
= from 05 30 to 12 00
= 6 h 30 min
= 6 ³⁰₆₀ h
= 6 ¹₂ h

Distance that Xylia cycled more than Yen
= 6¹₂ x 2
= ¹³₂ x 2
= 5 km

Yen's cycling speed
= 5 x 2
= 10 km/h

Xylia's cycling speed
= 10 + 2
= 12 km/h

Distance that Xylia cycled before she stopped to wait for Yen
= 194 - 38
= 156 km

Duration that Xylia cycled for after she caught up with Yen and when she stopped to wait for Yen
= (156 ÷ 12) - 6¹₂
= 13 - 6¹₂
= 6¹₂ h

Distance Yen was from Xylia when she stopped to wait
= 2 x 6¹₂
= 13 km

Answer(s): 13 km