Fabian left City R for City Q at 09 36. Shiyun left City R for City C at the same time. At 11 36, they were 408 km apart. Both maintained a constant speed and reached their destination at the same time at 13 16.

1. Find the distance between Cities A and C.
2. If Shiyun was ⁸₉ the speed of Fabian, find Fabian's speed.

(a)
Time taken for Fabian and Shiyun to travel 09 36 to 11 36 = 2 h
Time taken for Fabian and Shiyun to travel 09 36 to 13 16 = 3 h 40 min = 3⁴⁰₆₀ h = 3²₃ h

Distance travelled by Fabian and Shiyun in 1 hour
= 408 ÷ 2
= 204 km

Total distance
= 3²₃ x 204
= 748 km

(b)
Shiyun's distance : Fabian's distance
8 : 9

Shiyun's speed : Fabian's speed
8 : 9

17 u = 204 km
1 u = 204 ÷ 17 = 12 km

Fabian's speed
= 9 u
= 9 x 12
= 108 km/h

Answer(s): (a) 748 km; (b) 108km/h