The distance between Town C and Town D was 116 km. At 05 00, Lucy left Town C and cycled towards Town D. Xylia left Town C and cycled towards Town D at 05 30. Xylia's cycling speed was 2 km/h faster than Lucy. At 9 00, Xylia caught up with Lucy. When Xylia was 20 km from Town D, she stopped to wait for Lucy. How far was Lucy from Xylia when she stopped to wait for him?
Duration in which Xylia cycled for before she caught up with Lucy
= from 05 30 to 9 00
= 3 h 30 min
= 3 ³⁰₆₀ h
= 3 ¹₂ h

Distance that Xylia cycled more than Lucy
= 3¹₂ x 2
= ⁷₂ x 2
= 5 km

Lucy'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 Lucy
= 116 - 20
= 96 km

Duration that Xylia cycled for after she caught up with Lucy and when she stopped to wait for Lucy
= (96 ÷ 12) - 3¹₂
= 8 - 3¹₂
= 4¹₂ h

Distance Lucy was from Xylia when she stopped to wait
= 2 x 4¹₂
= 9 km

Answer(s): 9 km