A pastry shop and a flower shop, 1500 m apart, are situated between Xuan's house and Eva's house. The flower shop is halfway between the two houses and the pastry shop is closer to Eva's house. Xuan and Eva left their homes at the same time and arrived at the pastry shop at the same time. Xuan drove at a speed of 60 km/h while Eva drove at a speed 20 km/h slower than Xuan. Leaving your answer in kilometres,

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

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

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

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

Distance that Xuan travelled
= ³₂₀ x 60
= 9 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Eva's house and the flower shop
= 9 - 1.5
= 7.5 km

Answer(s): (a) 3 km; (b) 7.5 km