A church and a flower shop, 500 m apart, are situated between Xuan's house and Emma's house. The flower shop is halfway between the two houses and the church is closer to Emma's house. Xuan and Emma left their homes at the same time and arrived at the church at the same time. Xuan drove at a speed of 66 km/h while Emma drove at a speed 11 km/h slower than Xuan. Leaving your answer in kilometres,

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

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

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

(b)
Time that Xuan took to travel to the church
= 1 ÷ 11
= ¹₁₁ h

Distance that Xuan travelled
= ¹₁₁ x 66
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Emma's house and the flower shop
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km