A church and a flower shop, 500 m apart, are situated between Erika's house and Natalie's house. The flower shop is halfway between the two houses and the church is closer to Natalie's house. Erika and Natalie left their homes at the same time and arrived at the church at the same time. Erika drove at a speed of 67 km/h while Natalie drove at a speed 10 km/h slower than Erika. Leaving your answer in kilometres,

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

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

Distance that Erika travelled more than Natalie
= 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 67
= 6.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Natalie's house and the flower shop
= 6.7 - 0.5
= 6.2 km

Answer(s): (a) 1 km; (b) 6.2 km