The distance between Town P and Town Q was 171 km. At 05 00, Usha left Town P and cycled towards Town Q. Cathy left Town P and cycled towards Town Q at 05 30. Cathy's cycling speed was 2 km/h faster than Usha. At 12 00, Cathy caught up with Usha. When Cathy was 39 km from Town Q, she stopped to wait for Usha. How far was Usha from Cathy when she stopped to wait for him?
Duration in which Cathy cycled for before she caught up with Usha
= from 05 30 to 12 00
= 6 h 30 min
= 6 ³⁰₆₀ h
= 6 ¹₂ h

Distance that Cathy cycled more than Usha
= 6¹₂ x 2
= ¹³₂ x 2
= 5 km

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

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

Distance that Cathy cycled before she stopped to wait for Usha
= 171 - 39
= 132 km

Duration that Cathy cycled for after she caught up with Usha and when she stopped to wait for Usha
= (132 ÷ 12) - 6¹₂
= 11 - 6¹₂
= 4¹₂ h

Distance Usha was from Cathy when she stopped to wait
= 2 x 4¹₂
= 9 km

Answer(s): 9 km