Ethan left City E for City D at 08 34. Barbara left City E for City C at the same time. At 11 34, they were 480 km apart. Both maintained a constant speed and reached their destination at the same time at 13 22.

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

(a)
Time taken for Ethan and Barbara to travel 08 34 to 11 34 = 3 h
Time taken for Ethan and Barbara to travel 08 34 to 13 22 = 4 h 48 min = 4⁴⁸₆₀ h = 4⁴₅ h

Distance travelled by Ethan and Barbara in 1 hour
= 480 ÷ 3
= 160 km

Total distance
= 4⁴₅ x 160
= 768 km

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

Barbara's speed : Ethan's speed
3 : 5

8 u = 160 km
1 u = 160 ÷ 8 = 20 km

Ethan's speed
= 5 u
= 5 x 20
= 100 km/h

Answer(s): (a) 768 km; (b) 100km/h