The distance between Town L and Town M was 129 km. At 05 00, Emily left Town L and cycled towards Town M. Opal left Town L and cycled towards Town M at 05 30. Opal's cycling speed was 2 km/h faster than Emily. At 11 00, Opal caught up with Emily. When Opal was 21 km from Town M, she stopped to wait for Emily. How far was Emily from Opal when she stopped to wait for him?
Duration in which Opal cycled for before she caught up with Emily
= from 05 30 to 11 00
= 5 h 30 min
= 5 ³⁰₆₀ h
= 5 ¹₂ h

Distance that Opal cycled more than Emily
= 5¹₂ x 2
= ¹¹₂ x 2
= 5 km

Emily's cycling speed
= 5 x 2
= 10 km/h

Opal's cycling speed
= 10 + 2
= 12 km/h

Distance that Opal cycled before she stopped to wait for Emily
= 129 - 21
= 108 km

Duration that Opal cycled for after she caught up with Emily and when she stopped to wait for Emily
= (108 ÷ 12) - 5¹₂
= 9 - 5¹₂
= 3¹₂ h

Distance Emily was from Opal when she stopped to wait
= 2 x 3¹₂
= 7 km

Answer(s): 7 km