A pastry shop and a flower shop, 1500 m apart, are situated between Joelle's house and Betty's house. The flower shop is halfway between the two houses and the pastry shop is closer to Betty's house. Joelle and Betty left their homes at the same time and arrived at the pastry shop at the same time. Joelle drove at a speed of 61 km/h while Betty drove at a speed 10 km/h slower than Joelle. Leaving your answer in kilometres,

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

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

Distance that Joelle travelled more than Betty
= 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 ÷ 10
= ³₁₀ h

Distance that Joelle travelled
= ³₁₀ x 61
= 18.3 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Betty's house and the flower shop
= 18.3 - 1.5
= 16.8 km

Answer(s): (a) 3 km; (b) 16.8 km