A church and a flower shop, 500 m apart, are situated between Erika's house and Lucy's house. The flower shop is halfway between the two houses and the church is closer to Lucy's house. Erika and Lucy left their homes at the same time and arrived at the church at the same time. Erika drove at a speed of 76 km/h while Lucy drove at a speed 10 km/h slower than Erika. Leaving your answer in kilometres,

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

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

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

(b)
Time that Erika took to travel to the church
= 1 ÷ 10
= ¹₁₀ h

Distance that Erika travelled
= ¹₁₀ x 76
= 7.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lucy's house and the flower shop
= 7.6 - 0.5
= 7.1 km

Answer(s): (a) 1 km; (b) 7.1 km