A pastry shop and a flower shop, 3500 m apart, are situated between Jane's house and Nicole's house. The flower shop is halfway between the two houses and the pastry shop is closer to Nicole's house. Jane and Nicole left their homes at the same time and arrived at the pastry shop at the same time. Jane drove at a speed of 65 km/h while Nicole drove at a speed 20 km/h slower than Jane. Leaving your answer in kilometres,

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

(a)
Let the distance between Jane's house and Nicole's house be 1 d.
Nicole travelled = ¹₂ d - 3500 m
Jane travelled = ¹₂ d + 3500 m

Distance that Jane travelled more than Nicole
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Jane took to travel to the pastry shop
= 7 ÷ 20
= ⁷₂₀ h

Distance that Jane travelled
= ⁷₂₀ x 65
= 22.75 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Nicole's house and the flower shop
= 22.75 - 3.5
= 19.25 km

Answer(s): (a) 7 km; (b) 19.25 km