A pastry shop and a flower shop, 500 m apart, are situated between Zoe's house and Emma's house. The flower shop is halfway between the two houses and the pastry shop is closer to Emma's house. Zoe and Emma left their homes at the same time and arrived at the pastry shop at the same time. Zoe drove at a speed of 80 km/h while Emma drove at a speed 10 km/h slower than Zoe. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zoe took to travel to the pastry shop
= 1 ÷ 10
= ¹₁₀ h

Distance that Zoe travelled
= ¹₁₀ x 80
= 8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Emma's house and the flower shop
= 8 - 0.5
= 7.5 km

Answer(s): (a) 1 km; (b) 7.5 km