The distance between Town S and Town T was 165 km. At 05 00, Fanny left Town S and cycled towards Town T. Esther left Town S and cycled towards Town T at 05 40. Esther's cycling speed was 3 km/h faster than Fanny. At 9 00, Esther caught up with Fanny. When Esther was 21 km from Town T, she stopped to wait for Fanny. How far was Fanny from Esther when she stopped to wait for him?
Duration in which Esther cycled for before she caught up with Fanny
= from 05 40 to 9 00
= 3 h 20 min
= 3 ²⁰₆₀ h
= 3 ¹₃ h

Distance that Esther cycled more than Fanny
= 3¹₃ x 3
= ¹⁰₃ x 3
= 5 km

Fanny's cycling speed
= 5 x 3
= 15 km/h

Esther's cycling speed
= 15 + 3
= 18 km/h

Distance that Esther cycled before she stopped to wait for Fanny
= 165 - 21
= 144 km

Duration that Esther cycled for after she caught up with Fanny and when she stopped to wait for Fanny
= (144 ÷ 18) - 3¹₃
= 8 - 3¹₃
= 4²₃ h

Distance Fanny was from Esther when she stopped to wait
= 3 x 4²₃
= 14 km

Answer(s): 14 km