The distance between Town U and Town V was 200 km. At 08 00, Esther left Town U and cycled towards Town V. Xylia left Town U and cycled towards Town V at 08 45. Xylia's cycling speed was 4 km/h faster than Esther. At 11 00, Xylia caught up with Esther. When Xylia was 20 km from Town V, she stopped to wait for Esther. How far was Esther from Xylia when she stopped to wait for him?
Duration in which Xylia cycled for before she caught up with Esther
= from 08 45 to 11 00
= 2 h 15 min
= 2 ¹⁵₆₀ h
= 2 ¹₄ h

Distance that Xylia cycled more than Esther
= 2¹₄ x 4
= ⁹₄ x 4
= 8 km

Esther's cycling speed
= 8 x 4
= 32 km/h

Xylia's cycling speed
= 32 + 4
= 36 km/h

Distance that Xylia cycled before she stopped to wait for Esther
= 200 - 20
= 180 km

Duration that Xylia cycled for after she caught up with Esther and when she stopped to wait for Esther
= (180 ÷ 36) - 2¹₄
= 5 - 2¹₄
= 2³₄ h

Distance Esther was from Xylia when she stopped to wait
= 4 x 2³₄
= 11 km

Answer(s): 11 km