A church and a flower shop, 500 m apart, are situated between Julie's house and Olivia's house. The flower shop is halfway between the two houses and the church is closer to Olivia's house. Julie and Olivia left their homes at the same time and arrived at the church at the same time. Julie drove at a speed of 60 km/h while Olivia drove at a speed 20 km/h slower than Julie. Leaving your answer in kilometres,

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

(a)
Let the distance between Julie's house and Olivia's house be 1 d.
Olivia travelled = ¹₂ d - 500 m
Julie travelled = ¹₂ d + 500 m

Distance that Julie travelled more than Olivia
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Julie took to travel to the church
= 1 ÷ 20
= ¹₂₀ h

Distance that Julie travelled
= ¹₂₀ x 60
= 3 km

1000 m = 1 km
500 m = 0.5 km

Distance between Olivia's house and the flower shop
= 3 - 0.5
= 2.5 km

Answer(s): (a) 1 km; (b) 2.5 km