Neave started driving from City P towards City Q at 15 40 at an average speed of 60 km/h. Ethan began driving from City P towards City Q at 17 20 at an average speed of 100 km/h.

1. At what time did Ethan pass Neave on the road?
2. 1¹₄ hours after passing Neave, Ethan reached City Q. At what time did Neave reach City Q?

(a)
From 15 40 to 17 20 = 1 h 40 min

Time that Neave travelled before Ethan started driving = 1 h 40 min

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

Distance that Neave travelled before Ethan started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Ethan's and Neave's speed
= 100 - 60
= 40 km/h

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

2 h 30 min after 17 20 = 19 50

Time that Ethan passed Neave on the road = 19 50

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between City P and City Q
= 3³₄ x 100
= 375 km

Time that Neave travelled from City P to City Q
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 15 40 = 21 55

Time that Neave reached City Q = 21 55

Answer: (a) 19 50; (b) 21 55