The distance between Town Z and Town A was 180 km. At 05 00, Diana left Town Z and cycled towards Town A. Rachel left Town Z and cycled towards Town A at 05 20. Rachel's cycling speed was 3 km/h faster than Diana. At 11 00, Rachel caught up with Diana. When Rachel was 36 km from Town A, she stopped to wait for Diana. How far was Diana from Rachel when she stopped to wait for him?
Duration in which Rachel cycled for before she caught up with Diana
= from 05 20 to 11 00
= 5 h 40 min
= 5 ⁴⁰₆₀ h
= 5 ²₃ h

Distance that Rachel cycled more than Diana
= 5²₃ x 3
= ¹⁷₃ x 3
= 5 km

Diana's cycling speed
= 5 x 3
= 15 km/h

Rachel's cycling speed
= 15 + 3
= 18 km/h

Distance that Rachel cycled before she stopped to wait for Diana
= 180 - 36
= 144 km

Duration that Rachel cycled for after she caught up with Diana and when she stopped to wait for Diana
= (144 ÷ 18) - 5²₃
= 8 - 5²₃
= 2¹₃ h

Distance Diana was from Rachel when she stopped to wait
= 3 x 2¹₃
= 7 km

Answer(s): 7 km