Henry left City Z for City Y at 08 17. Barbara left City Z for City C at the same time. At 10 17, they were 336 km apart. Both maintained a constant speed and reached their destination at the same time at 15 12.

1. Find the distance between Cities A and C.
2. If Barbara was ³₅ the speed of Henry, find Henry's speed.

(a)
Time taken for Henry and Barbara to travel 08 17 to 10 17 = 2 h
Time taken for Henry and Barbara to travel 08 17 to 15 12 = 6 h 55 min = 6⁵⁵₆₀ h = 6¹¹₁₂ h

Distance travelled by Henry and Barbara in 1 hour
= 336 ÷ 2
= 168 km

Total distance
= 6¹¹₁₂ x 168
= 1162 km

(b)
Barbara's distance : Henry's distance
3 : 5

Barbara's speed : Henry's speed
3 : 5

8 u = 168 km
1 u = 168 ÷ 8 = 21 km

Henry's speed
= 5 u
= 5 x 21
= 105 km/h

Answer(s): (a) 1162 km; (b) 105km/h