Pierre left City T for City S at 09 37. Natalie left City T for City C at the same time. At 13 37, they were 760 km apart. Both maintained a constant speed and reached their destination at the same time at 15 13.

1. Find the distance between Cities A and C.
2. If Natalie was ⁹₁₀ the speed of Pierre, find Pierre's speed.

(a)
Time taken for Pierre and Natalie to travel 09 37 to 13 37 = 4 h
Time taken for Pierre and Natalie to travel 09 37 to 15 13 = 5 h 36 min = 5³⁶₆₀ h = 5³₅ h

Distance travelled by Pierre and Natalie in 1 hour
= 760 ÷ 4
= 190 km

Total distance
= 5³₅ x 190
= 1064 km

(b)
Natalie's distance : Pierre's distance
9 : 10

Natalie's speed : Pierre's speed
9 : 10

19 u = 190 km
1 u = 190 ÷ 19 = 10 km

Pierre's speed
= 10 u
= 10 x 10
= 100 km/h

Answer(s): (a) 1064 km; (b) 100km/h