A church and a flower shop, 1500 m apart, are situated between Kylie's house and Kathy's house. The flower shop is halfway between the two houses and the church is closer to Kathy's house. Kylie and Kathy left their homes at the same time and arrived at the church at the same time. Kylie drove at a speed of 63 km/h while Kathy drove at a speed 10 km/h slower than Kylie. Leaving your answer in kilometres,

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

(a)
Let the distance between Kylie's house and Kathy's house be 1 d.
Kathy travelled = ¹₂ d - 1500 m
Kylie travelled = ¹₂ d + 1500 m

Distance that Kylie travelled more than Kathy
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Kylie took to travel to the church
= 3 ÷ 10
= ³₁₀ h

Distance that Kylie travelled
= ³₁₀ x 63
= 18.9 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kathy's house and the flower shop
= 18.9 - 1.5
= 17.4 km

Answer(s): (a) 3 km; (b) 17.4 km