A pastry shop and a flower shop, 500 m apart, are situated between Erika'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. Erika and Emma left their homes at the same time and arrived at the pastry shop at the same time. Erika drove at a speed of 80 km/h while Emma drove at a speed 20 km/h slower than Erika. Leaving your answer in kilometres,

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

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

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

(b)
Time that Erika took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Erika travelled
= ¹₂₀ x 80
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Emma's house and the flower shop
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km