A church and a flower shop, 3500 m apart, are situated between Nicole's house and Sarah's house. The flower shop is halfway between the two houses and the church is closer to Sarah's house. Nicole and Sarah left their homes at the same time and arrived at the church at the same time. Nicole drove at a speed of 66 km/h while Sarah drove at a speed 20 km/h slower than Nicole. Leaving your answer in kilometres,

1. how much farther did Nicole travel than Sarah?
2. how far is Sarah's house from the flower shop?

(a)
Let the distance between Nicole's house and Sarah's house be 1 d.
Sarah travelled = ¹₂ d - 3500 m
Nicole travelled = ¹₂ d + 3500 m

Distance that Nicole travelled more than Sarah
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Nicole took to travel to the church
= 7 ÷ 20
= ⁷₂₀ h

Distance that Nicole travelled
= ⁷₂₀ x 66
= 23.1 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Sarah's house and the flower shop
= 23.1 - 3.5
= 19.6 km

Answer(s): (a) 7 km; (b) 19.6 km