The distance between Town X and Town Y was 136 km. At 06 00, Irene left Town X and cycled towards Town Y. Kathy left Town X and cycled towards Town Y at 06 30. Kathy's cycling speed was 4 km/h faster than Irene. At 9 00, Kathy caught up with Irene. When Kathy was 24 km from Town Y, she stopped to wait for Irene. How far was Irene from Kathy when she stopped to wait for him?
Duration in which Kathy cycled for before she caught up with Irene
= from 06 30 to 9 00
= 2 h 30 min
= 2 ³⁰₆₀ h
= 2 ¹₂ h

Distance that Kathy cycled more than Irene
= 2¹₂ x 4
= ⁵₂ x 4
= 6 km

Irene's cycling speed
= 6 x 4
= 24 km/h

Kathy's cycling speed
= 24 + 4
= 28 km/h

Distance that Kathy cycled before she stopped to wait for Irene
= 136 - 24
= 112 km

Duration that Kathy cycled for after she caught up with Irene and when she stopped to wait for Irene
= (112 ÷ 28) - 2¹₂
= 4 - 2¹₂
= 1¹₂ h

Distance Irene was from Kathy when she stopped to wait
= 4 x 1¹₂
= 6 km

Answer(s): 6 km