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

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

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

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

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

Distance that Sarah travelled
= ⁵₁₄ x 63
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

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

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