A pastry shop and a flower shop, 1500 m apart, are situated between Sabrina's house and Marion's house. The flower shop is halfway between the two houses and the pastry shop is closer to Marion's house. Sabrina and Marion left their homes at the same time and arrived at the pastry shop at the same time. Sabrina drove at a speed of 70 km/h while Marion drove at a speed 20 km/h slower than Sabrina. Leaving your answer in kilometres,

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

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

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

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

Distance that Sabrina travelled
= ³₂₀ x 70
= 10.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Marion's house and the flower shop
= 10.5 - 1.5
= 9 km

Answer(s): (a) 3 km; (b) 9 km