A pastry shop and a flower shop, 1500 m apart, are situated between Fiona's house and Ivory's house. The flower shop is halfway between the two houses and the pastry shop is closer to Ivory's house. Fiona and Ivory left their homes at the same time and arrived at the pastry shop at the same time. Fiona drove at a speed of 72 km/h while Ivory drove at a speed 20 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

(b)
Time that Fiona took to travel to the pastry shop
= 3 ÷ 20
= ³₂₀ h

Distance that Fiona travelled
= ³₂₀ x 72
= 10.8 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Ivory's house and the flower shop
= 10.8 - 1.5
= 9.3 km

Answer(s): (a) 3 km; (b) 9.3 km