A church and a flower shop, 2500 m apart, are situated between Victoria's house and Zara's house. The flower shop is halfway between the two houses and the church is closer to Zara's house. Victoria and Zara left their homes at the same time and arrived at the church at the same time. Victoria drove at a speed of 63 km/h while Zara drove at a speed 14 km/h slower than Victoria. Leaving your answer in kilometres,

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

(a)
Let the distance between Victoria's house and Zara's house be 1 d.
Zara travelled = ¹₂ d - 2500 m
Victoria travelled = ¹₂ d + 2500 m

Distance that Victoria travelled more than Zara
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Victoria took to travel to the church
= 5 ÷ 14
= ⁵₁₄ h

Distance that Victoria travelled
= ⁵₁₄ x 63
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Zara's house and the flower shop
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km