Pierre started driving from Town U towards Town V at 14 40 at an average speed of 60 km/h. Paul began driving from Town U towards Town V at 16 20 at an average speed of 100 km/h.

1. At what time did Paul pass Pierre on the road?
2. 1¹₄ hours after passing Pierre, Paul reached Town V. At what time did Pierre reach Town V?

(a)
From 14 40 to 16 20 = 1 h 40 min

Time that Pierre travelled before Paul started driving = 1 h 40 min

1 h = 60 min
1 h 40 min = 1⁴⁰₆₀ h = 1²₃ h

Distance that Pierre travelled before Paul started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Paul's and Pierre's speed
= 100 - 60
= 40 km/h

Time that Paul took to catch up with Pierre
= 100 ÷ 40
= 2.5 h
= 2 h 30 min

2 h 30 min after 16 20 = 18 50

Time that Paul passed Pierre on the road = 18 50

(b)
1¹₄ h = 1 h 15 min

Total time that Paul travelled
= 1 h 15 min + 2 h 30 min
= 3 h 45 min

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Town U and Town V
= 3³₄ x 100
= 375 km

Time that Pierre travelled from Town U to Town V
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 14 40 = 20 55

Time that Pierre reached Town V = 20 55

Answer: (a) 18 50; (b) 20 55