A pastry shop and a flower shop, 3500 m apart, are situated between Natalie's house and Sabrina's house. The flower shop is halfway between the two houses and the pastry shop is closer to Sabrina's house. Natalie and Sabrina left their homes at the same time and arrived at the pastry shop at the same time. Natalie drove at a speed of 66 km/h while Sabrina drove at a speed 20 km/h slower than Natalie. Leaving your answer in kilometres,

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

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

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

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

Distance that Natalie travelled
= ⁷₂₀ x 66
= 23.1 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Sabrina's house and the flower shop
= 23.1 - 3.5
= 19.6 km

Answer(s): (a) 7 km; (b) 19.6 km