A church and a flower shop, 500 m apart, are situated between Fiona's house and Dana's house. The flower shop is halfway between the two houses and the church is closer to Dana's house. Fiona and Dana left their homes at the same time and arrived at the church at the same time. Fiona drove at a speed of 64 km/h while Dana drove at a speed 10 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

Distance that Fiona travelled more than Dana
= 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 ÷ 10
= ¹₁₀ h

Distance that Fiona travelled
= ¹₁₀ x 64
= 6.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Dana's house and the flower shop
= 6.4 - 0.5
= 5.9 km

Answer(s): (a) 1 km; (b) 5.9 km