A pastry shop and a flower shop, 500 m apart, are situated between Marion's house and Emily's house. The flower shop is halfway between the two houses and the pastry shop is closer to Emily's house. Marion and Emily left their homes at the same time and arrived at the pastry shop at the same time. Marion drove at a speed of 67 km/h while Emily drove at a speed 20 km/h slower than Marion. Leaving your answer in kilometres,

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

(a)
Let the distance between Marion's house and Emily's house be 1 d.
Emily travelled = ¹₂ d - 500 m
Marion travelled = ¹₂ d + 500 m

Distance that Marion travelled more than Emily
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Marion took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Marion travelled
= ¹₂₀ x 67
= 3.35 km

1000 m = 1 km
500 m = 0.5 km

Distance between Emily's house and the flower shop
= 3.35 - 0.5
= 2.85 km

Answer(s): (a) 1 km; (b) 2.85 km