Ahmad left City K for City J at 09 49. Vanessa left City K for City C at the same time. At 11 49, they were 420 km apart. Both maintained a constant speed and reached their destination at the same time at 15 43.

1. Find the distance between Cities A and C.
2. If Vanessa was ⁷₈ the speed of Ahmad, find Ahmad's speed.

(a)
Time taken for Ahmad and Vanessa to travel 09 49 to 11 49 = 2 h
Time taken for Ahmad and Vanessa to travel 09 49 to 15 43 = 5 h 54 min = 5⁵⁴₆₀ h = 5⁹₁₀ h

Distance travelled by Ahmad and Vanessa in 1 hour
= 420 ÷ 2
= 210 km

Total distance
= 5⁹₁₀ x 210
= 1239 km

(b)
Vanessa's distance : Ahmad's distance
7 : 8

Vanessa's speed : Ahmad's speed
7 : 8

15 u = 210 km
1 u = 210 ÷ 15 = 14 km

Ahmad's speed
= 8 u
= 8 x 14
= 112 km/h

Answer(s): (a) 1239 km; (b) 112km/h