Riordan started driving from Town Y towards Town Z at 15 30 at an average speed of 60 km/h. Pierre began driving from Town Y towards Town Z at 17 10 at an average speed of 100 km/h.

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

(a)
From 15 30 to 17 10 = 1 h 40 min

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

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

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

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

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

2 h 30 min after 17 10 = 19 40

Time that Pierre passed Riordan on the road = 19 40

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Town Y and Town Z
= 3³₄ x 100
= 375 km

Time that Riordan travelled from Town Y to Town Z
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 15 30 = 21 45

Time that Riordan reached Town Z = 21 45

Answer: (a) 19 40; (b) 21 45