A church and a flower shop, 500 m apart, are situated between Xandra's house and Opal's house. The flower shop is halfway between the two houses and the church is closer to Opal's house. Xandra and Opal left their homes at the same time and arrived at the church at the same time. Xandra drove at a speed of 62 km/h while Opal drove at a speed 20 km/h slower than Xandra. Leaving your answer in kilometres,

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

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

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

(b)
Time that Xandra took to travel to the church
= 1 ÷ 20
= ¹₂₀ h

Distance that Xandra travelled
= ¹₂₀ x 62
= 3.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Opal's house and the flower shop
= 3.1 - 0.5
= 2.6 km

Answer(s): (a) 1 km; (b) 2.6 km