A pastry shop and a flower shop, 3500 m apart, are situated between Nora'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. Nora and Olivia left their homes at the same time and arrived at the pastry shop at the same time. Nora drove at a speed of 61 km/h while Olivia drove at a speed 20 km/h slower than Nora. Leaving your answer in kilometres,

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

(a)
Let the distance between Nora's house and Olivia's house be 1 d.
Olivia travelled = ¹₂ d - 3500 m
Nora travelled = ¹₂ d + 3500 m

Distance that Nora travelled more than Olivia
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Nora took to travel to the pastry shop
= 7 ÷ 20
= ⁷₂₀ h

Distance that Nora travelled
= ⁷₂₀ x 61
= 21.35 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Olivia's house and the flower shop
= 21.35 - 3.5
= 17.85 km

Answer(s): (a) 7 km; (b) 17.85 km