A church and a flower shop, 500 m apart, are situated between Victoria's house and Fanny's house. The flower shop is halfway between the two houses and the church is closer to Fanny's house. Victoria and Fanny left their homes at the same time and arrived at the church at the same time. Victoria drove at a speed of 69 km/h while Fanny drove at a speed 15 km/h slower than Victoria. Leaving your answer in kilometres,

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

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

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

(b)
Time that Victoria took to travel to the church
= 1 ÷ 15
= ¹₁₅ h

Distance that Victoria travelled
= ¹₁₅ x 69
= 4.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Fanny's house and the flower shop
= 4.6 - 0.5
= 4.1 km

Answer(s): (a) 1 km; (b) 4.1 km