A pastry shop and a flower shop, 500 m apart, are situated between Joelle's house and Lucy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Lucy's house. Joelle and Lucy left their homes at the same time and arrived at the pastry shop at the same time. Joelle drove at a speed of 78 km/h while Lucy drove at a speed 20 km/h slower than Joelle. Leaving your answer in kilometres,

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

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

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

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

Distance that Joelle travelled
= ¹₂₀ x 78
= 3.9 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lucy's house and the flower shop
= 3.9 - 0.5
= 3.4 km

Answer(s): (a) 1 km; (b) 3.4 km