A pastry shop and a flower shop, 1500 m apart, are situated between Kimberly's house and Olivia's house. The flower shop is halfway between the two houses and the pastry shop is closer to Olivia's house. Kimberly and Olivia left their homes at the same time and arrived at the pastry shop at the same time. Kimberly drove at a speed of 62 km/h while Olivia drove at a speed 20 km/h slower than Kimberly. Leaving your answer in kilometres,

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

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

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

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

Distance that Kimberly travelled
= ³₂₀ x 62
= 9.3 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Olivia's house and the flower shop
= 9.3 - 1.5
= 7.8 km

Answer(s): (a) 3 km; (b) 7.8 km