Julian left City K for City J at 05 25. Esther left City K for City C at the same time. At 10 25, they were 975 km apart. Both maintained a constant speed and reached their destination at the same time at 12 13.

1. Find the distance between Cities A and C.
2. If Esther was ⁶₇ the speed of Julian, find Julian's speed.

(a)
Time taken for Julian and Esther to travel 05 25 to 10 25 = 5 h
Time taken for Julian and Esther to travel 05 25 to 12 13 = 6 h 48 min = 6⁴⁸₆₀ h = 6⁴₅ h

Distance travelled by Julian and Esther in 1 hour
= 975 ÷ 5
= 195 km

Total distance
= 6⁴₅ x 195
= 1326 km

(b)
Esther's distance : Julian's distance
6 : 7

Esther's speed : Julian's speed
6 : 7

13 u = 195 km
1 u = 195 ÷ 13 = 15 km

Julian's speed
= 7 u
= 7 x 15
= 105 km/h

Answer(s): (a) 1326 km; (b) 105km/h