A church and a flower shop, 500 m apart, are situated between Zoe's house and Lucy's house. The flower shop is halfway between the two houses and the church is closer to Lucy's house. Zoe and Lucy left their homes at the same time and arrived at the church at the same time. Zoe drove at a speed of 76 km/h while Lucy drove at a speed 16 km/h slower than Zoe. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zoe took to travel to the church
= 1 ÷ 16
= ¹₁₆ h

Distance that Zoe travelled
= ¹₁₆ x 76
= 4.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lucy's house and the flower shop
= 4.75 - 0.5
= 4.25 km

Answer(s): (a) 1 km; (b) 4.25 km