The distance between Town C and Town D was 142 km. At 08 00, Vanessa left Town C and cycled towards Town D. Cathy left Town C and cycled towards Town D at 08 30. Cathy's cycling speed was 2 km/h faster than Vanessa. At 13 00, Cathy caught up with Vanessa. When Cathy was 16 km from Town D, she stopped to wait for Vanessa. How far was Vanessa from Cathy when she stopped to wait for him?
Duration in which Cathy cycled for before she caught up with Vanessa
= from 08 30 to 13 00
= 4 h 30 min
= 4 ³⁰₆₀ h
= 4 ¹₂ h

Distance that Cathy cycled more than Vanessa
= 4¹₂ x 2
= ⁹₂ x 2
= 8 km

Vanessa's cycling speed
= 8 x 2
= 16 km/h

Cathy's cycling speed
= 16 + 2
= 18 km/h

Distance that Cathy cycled before she stopped to wait for Vanessa
= 142 - 16
= 126 km

Duration that Cathy cycled for after she caught up with Vanessa and when she stopped to wait for Vanessa
= (126 ÷ 18) - 4¹₂
= 7 - 4¹₂
= 2¹₂ h

Distance Vanessa was from Cathy when she stopped to wait
= 2 x 2¹₂
= 5 km

Answer(s): 5 km