A pastry shop and a flower shop, 1500 m apart, are situated between Joelle's house and Fanny's house. The flower shop is halfway between the two houses and the pastry shop is closer to Fanny's house. Joelle and Fanny 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 Fanny drove at a speed 13 km/h slower than Joelle. Leaving your answer in kilometres,

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

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

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

(b)
Time that Joelle took to travel to the pastry shop
= 3 ÷ 13
= ³₁₃ h

Distance that Joelle travelled
= ³₁₃ x 78
= 18 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Fanny's house and the flower shop
= 18 - 1.5
= 16.5 km

Answer(s): (a) 3 km; (b) 16.5 km