The distance between Town P and Town Q was 199 km. At 07 00, Irene left Town P and cycled towards Town Q. Fanny left Town P and cycled towards Town Q at 07 20. Fanny's cycling speed was 3 km/h faster than Irene. At 10 00, Fanny caught up with Irene. When Fanny was 31 km from Town Q, she stopped to wait for Irene. How far was Irene from Fanny when she stopped to wait for him?
Duration in which Fanny cycled for before she caught up with Irene
= from 07 20 to 10 00
= 2 h 40 min
= 2 ⁴⁰₆₀ h
= 2 ²₃ h

Distance that Fanny cycled more than Irene
= 2²₃ x 3
= ⁸₃ x 3
= 7 km

Irene's cycling speed
= 7 x 3
= 21 km/h

Fanny's cycling speed
= 21 + 3
= 24 km/h

Distance that Fanny cycled before she stopped to wait for Irene
= 199 - 31
= 168 km

Duration that Fanny cycled for after she caught up with Irene and when she stopped to wait for Irene
= (168 ÷ 24) - 2²₃
= 7 - 2²₃
= 4¹₃ h

Distance Irene was from Fanny when she stopped to wait
= 3 x 4¹₃
= 13 km

Answer(s): 13 km