Jenson left City R for City Q at 07 37. Olivia left City R for City C at the same time. At 10 37, they were 540 km apart. Both maintained a constant speed and reached their destination at the same time at 12 29.

1. Find the distance between Cities A and C.
2. If Olivia was ⁴₅ the speed of Jenson, find Jenson's speed.

(a)
Time taken for Jenson and Olivia to travel 07 37 to 10 37 = 3 h
Time taken for Jenson and Olivia to travel 07 37 to 12 29 = 4 h 52 min = 4⁵²₆₀ h = 4¹³₁₅ h

Distance travelled by Jenson and Olivia in 1 hour
= 540 ÷ 3
= 180 km

Total distance
= 4¹³₁₅ x 180
= 876 km

(b)
Olivia's distance : Jenson's distance
4 : 5

Olivia's speed : Jenson's speed
4 : 5

9 u = 180 km
1 u = 180 ÷ 9 = 20 km

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

Answer(s): (a) 876 km; (b) 100km/h