A pastry shop and a flower shop, 500 m apart, are situated between Hilda's house and Joelle's house. The flower shop is halfway between the two houses and the pastry shop is closer to Joelle's house. Hilda and Joelle left their homes at the same time and arrived at the pastry shop at the same time. Hilda drove at a speed of 80 km/h while Joelle drove at a speed 20 km/h slower than Hilda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Hilda took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Hilda travelled
= ¹₂₀ x 80
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Joelle's house and the flower shop
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km