A pastry shop and a flower shop, 1500 m apart, are situated between Zoe'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. Zoe and Nicole left their homes at the same time and arrived at the pastry shop at the same time. Zoe drove at a speed of 77 km/h while Nicole drove at a speed 20 km/h slower than Zoe. Leaving your answer in kilometres,

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

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

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

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

Distance that Zoe travelled
= ³₂₀ x 77
= 11.55 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Nicole's house and the flower shop
= 11.55 - 1.5
= 10.05 km

Answer(s): (a) 3 km; (b) 10.05 km