The distance between Town D and Town E was 130 km. At 06 00, Gem left Town D and cycled towards Town E. Kylie left Town D and cycled towards Town E at 06 30. Kylie's cycling speed was 2 km/h faster than Gem. At 10 00, Kylie caught up with Gem. When Kylie was 18 km from Town E, she stopped to wait for Gem. How far was Gem from Kylie when she stopped to wait for him?
Duration in which Kylie cycled for before she caught up with Gem
= from 06 30 to 10 00
= 3 h 30 min
= 3 ³⁰₆₀ h
= 3 ¹₂ h

Distance that Kylie cycled more than Gem
= 3¹₂ x 2
= ⁷₂ x 2
= 6 km

Gem's cycling speed
= 6 x 2
= 12 km/h

Kylie's cycling speed
= 12 + 2
= 14 km/h

Distance that Kylie cycled before she stopped to wait for Gem
= 130 - 18
= 112 km

Duration that Kylie cycled for after she caught up with Gem and when she stopped to wait for Gem
= (112 ÷ 14) - 3¹₂
= 8 - 3¹₂
= 4¹₂ h

Distance Gem was from Kylie when she stopped to wait
= 2 x 4¹₂
= 9 km

Answer(s): 9 km