A church and a flower shop, 500 m apart, are situated between Xylia's house and Irene's house. The flower shop is halfway between the two houses and the church is closer to Irene's house. Xylia and Irene left their homes at the same time and arrived at the church at the same time. Xylia drove at a speed of 60 km/h while Irene drove at a speed 12 km/h slower than Xylia. Leaving your answer in kilometres,

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

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

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

(b)
Time that Xylia took to travel to the church
= 1 ÷ 12
= ¹₁₂ h

Distance that Xylia travelled
= ¹₁₂ x 60
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Irene's house and the flower shop
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km