A church and a flower shop, 500 m apart, are situated between Fiona's house and Abi's house. The flower shop is halfway between the two houses and the church is closer to Abi's house. Fiona and Abi left their homes at the same time and arrived at the church at the same time. Fiona drove at a speed of 74 km/h while Abi drove at a speed 20 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

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

Distance that Fiona travelled
= ¹₂₀ x 74
= 3.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Abi's house and the flower shop
= 3.7 - 0.5
= 3.2 km

Answer(s): (a) 1 km; (b) 3.2 km