A church and a flower shop, 1500 m apart, are situated between Hazel's house and Barbara's house. The flower shop is halfway between the two houses and the church is closer to Barbara's house. Hazel and Barbara left their homes at the same time and arrived at the church at the same time. Hazel drove at a speed of 63 km/h while Barbara drove at a speed 20 km/h slower than Hazel. Leaving your answer in kilometres,

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

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

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

(b)
Time that Hazel took to travel to the church
= 3 ÷ 20
= ³₂₀ h

Distance that Hazel travelled
= ³₂₀ x 63
= 9.45 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Barbara's house and the flower shop
= 9.45 - 1.5
= 7.95 km

Answer(s): (a) 3 km; (b) 7.95 km