Jenson left City Q for City P at 08 47. Esther left City Q for City C at the same time. At 11 47, they were 480 km apart. Both maintained a constant speed and reached their destination at the same time at 15 35.

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

(a)
Time taken for Jenson and Esther to travel 08 47 to 11 47 = 3 h
Time taken for Jenson and Esther to travel 08 47 to 15 35 = 6 h 48 min = 6⁴⁸₆₀ h = 6⁴₅ h

Distance travelled by Jenson and Esther in 1 hour
= 480 ÷ 3
= 160 km

Total distance
= 6⁴₅ x 160
= 1088 km

(b)
Esther's distance : Jenson's distance
3 : 5

Esther's speed : Jenson's speed
3 : 5

8 u = 160 km
1 u = 160 ÷ 8 = 20 km

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

Answer(s): (a) 1088 km; (b) 100km/h