A pastry shop and a flower shop, 500 m apart, are situated between Fiona's house and Diana's house. The flower shop is halfway between the two houses and the pastry shop is closer to Diana's house. Fiona and Diana left their homes at the same time and arrived at the pastry shop at the same time. Fiona drove at a speed of 70 km/h while Diana drove at a speed 20 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

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

Distance that Fiona travelled
= ¹₂₀ x 70
= 3.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Diana's house and the flower shop
= 3.5 - 0.5
= 3 km

Answer(s): (a) 1 km; (b) 3 km