A church and a flower shop, 1500 m apart, are situated between Lucy's house and Kimberly's house. The flower shop is halfway between the two houses and the church is closer to Kimberly's house. Lucy and Kimberly left their homes at the same time and arrived at the church at the same time. Lucy drove at a speed of 68 km/h while Kimberly drove at a speed 20 km/h slower than Lucy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Lucy took to travel to the church
= 3 ÷ 20
= ³₂₀ h

Distance that Lucy travelled
= ³₂₀ x 68
= 10.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kimberly's house and the flower shop
= 10.2 - 1.5
= 8.7 km

Answer(s): (a) 3 km; (b) 8.7 km