A church and a flower shop, 1500 m apart, are situated between Emily's house and Emma's house. The flower shop is halfway between the two houses and the church is closer to Emma's house. Emily and Emma left their homes at the same time and arrived at the church at the same time. Emily drove at a speed of 64 km/h while Emma drove at a speed 20 km/h slower than Emily. Leaving your answer in kilometres,

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

(a)
Let the distance between Emily's house and Emma's house be 1 d.
Emma travelled = ¹₂ d - 1500 m
Emily travelled = ¹₂ d + 1500 m

Distance that Emily travelled more than Emma
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Emily took to travel to the church
= 3 ÷ 20
= ³₂₀ h

Distance that Emily travelled
= ³₂₀ x 64
= 9.6 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Emma's house and the flower shop
= 9.6 - 1.5
= 8.1 km

Answer(s): (a) 3 km; (b) 8.1 km