Jack started driving from Town S towards Town T at 14 30 at an average speed of 60 km/h. Ivan began driving from Town S towards Town T at 16 10 at an average speed of 100 km/h.

1. At what time did Ivan pass Jack on the road?
2. 1¹₄ hours after passing Jack, Ivan reached Town T. At what time did Jack reach Town T?

(a)
From 14 30 to 16 10 = 1 h 40 min

Time that Jack travelled before Ivan started driving = 1 h 40 min

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

Distance that Jack travelled before Ivan started driving
= 1²₃ x 60
= ⁵₃ x 60
= 100 km

Difference between Ivan's and Jack's speed
= 100 - 60
= 40 km/h

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

2 h 30 min after 16 10 = 18 40

Time that Ivan passed Jack on the road = 18 40

(b)
1¹₄ h = 1 h 15 min

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

3 h 45 min = 3⁴⁵₆₀h = 3³₄h

Distance between Town S and Town T
= 3³₄ x 100
= 375 km

Time that Jack travelled from Town S to Town T
= 375 ÷ 60
= 6.25 h
= 6 h 15 min

6 h 15 min after 14 30 = 20 45

Time that Jack reached Town T = 20 45

Answer: (a) 18 40; (b) 20 45