A pastry shop and a flower shop, 1500 m apart, are situated between Hazel's house and Natalie's house. The flower shop is halfway between the two houses and the pastry shop is closer to Natalie's house. Hazel and Natalie left their homes at the same time and arrived at the pastry shop at the same time. Hazel drove at a speed of 67 km/h while Natalie drove at a speed 20 km/h slower than Hazel. Leaving your answer in kilometres,

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

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

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

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

Distance that Hazel travelled
= ³₂₀ x 67
= 10.05 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Natalie's house and the flower shop
= 10.05 - 1.5
= 8.55 km

Answer(s): (a) 3 km; (b) 8.55 km