A church and a flower shop, 500 m apart, are situated between Betty's house and Anna's house. The flower shop is halfway between the two houses and the church is closer to Anna's house. Betty and Anna left their homes at the same time and arrived at the church at the same time. Betty drove at a speed of 71 km/h while Anna drove at a speed 20 km/h slower than Betty. Leaving your answer in kilometres,

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

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

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

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

Distance that Betty travelled
= ¹₂₀ x 71
= 3.55 km

1000 m = 1 km
500 m = 0.5 km

Distance between Anna's house and the flower shop
= 3.55 - 0.5
= 3.05 km

Answer(s): (a) 1 km; (b) 3.05 km