Jeremy left City Q for City P at 08 47. Nicole left City Q for City C at the same time. At 11 47, they were 540 km apart. Both maintained a constant speed and reached their destination at the same time at 13 42.

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

(a)
Time taken for Jeremy and Nicole to travel 08 47 to 11 47 = 3 h
Time taken for Jeremy and Nicole to travel 08 47 to 13 42 = 4 h 55 min = 4⁵⁵₆₀ h = 4¹¹₁₂ h

Distance travelled by Jeremy and Nicole in 1 hour
= 540 ÷ 3
= 180 km

Total distance
= 4¹¹₁₂ x 180
= 885 km

(b)
Nicole's distance : Jeremy's distance
7 : 8

Nicole's speed : Jeremy's speed
7 : 8

15 u = 180 km
1 u = 180 ÷ 15 = 12 km

Jeremy's speed
= 8 u
= 8 x 12
= 96 km/h

Answer(s): (a) 885 km; (b) 96km/h