A church and a flower shop, 500 m apart, are situated between Emma's house and Zara's house. The flower shop is halfway between the two houses and the church is closer to Zara's house. Emma and Zara left their homes at the same time and arrived at the church at the same time. Emma drove at a speed of 71 km/h while Zara drove at a speed 10 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the church
= 1 ÷ 10
= ¹₁₀ h

Distance that Emma travelled
= ¹₁₀ x 71
= 7.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Zara's house and the flower shop
= 7.1 - 0.5
= 6.6 km

Answer(s): (a) 1 km; (b) 6.6 km