A pastry shop and a flower shop, 500 m apart, are situated between Nicole's house and Gillian's house. The flower shop is halfway between the two houses and the pastry shop is closer to Gillian's house. Nicole and Gillian left their homes at the same time and arrived at the pastry shop at the same time. Nicole drove at a speed of 60 km/h while Gillian drove at a speed 12 km/h slower than Nicole. Leaving your answer in kilometres,

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

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

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

(b)
Time that Nicole took to travel to the pastry shop
= 1 ÷ 12
= ¹₁₂ h

Distance that Nicole travelled
= ¹₁₂ x 60
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Gillian's house and the flower shop
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km