The distance between Town X and Town Y was 145 km. At 05 00, Penelope left Town X and cycled towards Town Y. Xuan left Town X and cycled towards Town Y at 05 30. Xuan's cycling speed was 2 km/h faster than Penelope. At 13 00, Xuan caught up with Penelope. When Xuan was 25 km from Town Y, she stopped to wait for Penelope. How far was Penelope from Xuan when she stopped to wait for him?
Duration in which Xuan cycled for before she caught up with Penelope
= from 05 30 to 13 00
= 7 h 30 min
= 7 ³⁰₆₀ h
= 7 ¹₂ h

Distance that Xuan cycled more than Penelope
= 7¹₂ x 2
= ¹⁵₂ x 2
= 5 km

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

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

Distance that Xuan cycled before she stopped to wait for Penelope
= 145 - 25
= 120 km

Duration that Xuan cycled for after she caught up with Penelope and when she stopped to wait for Penelope
= (120 ÷ 12) - 7¹₂
= 10 - 7¹₂
= 2¹₂ h

Distance Penelope was from Xuan when she stopped to wait
= 2 x 2¹₂
= 5 km

Answer(s): 5 km