A pastry shop and a flower shop, 1500 m apart, are situated between Anna'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. Anna and Emily left their homes at the same time and arrived at the pastry shop at the same time. Anna drove at a speed of 72 km/h while Emily drove at a speed 20 km/h slower than Anna. Leaving your answer in kilometres,

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

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

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

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

Distance that Anna travelled
= ³₂₀ x 72
= 10.8 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Emily's house and the flower shop
= 10.8 - 1.5
= 9.3 km

Answer(s): (a) 3 km; (b) 9.3 km