A church and a flower shop, 1500 m apart, are situated between Emma's house and Natalie's house. The flower shop is halfway between the two houses and the church is closer to Natalie's house. Emma and Natalie left their homes at the same time and arrived at the church at the same time. Emma drove at a speed of 68 km/h while Natalie drove at a speed 10 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the church
= 3 ÷ 10
= ³₁₀ h

Distance that Emma travelled
= ³₁₀ x 68
= 20.4 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Natalie's house and the flower shop
= 20.4 - 1.5
= 18.9 km

Answer(s): (a) 3 km; (b) 18.9 km