A church and a flower shop, 500 m apart, are situated between Eva's house and Cindy's house. The flower shop is halfway between the two houses and the church is closer to Cindy's house. Eva and Cindy left their homes at the same time and arrived at the church at the same time. Eva drove at a speed of 70 km/h while Cindy drove at a speed 10 km/h slower than Eva. Leaving your answer in kilometres,

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

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

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

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

Distance that Eva travelled
= ¹₁₀ x 70
= 7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Cindy's house and the flower shop
= 7 - 0.5
= 6.5 km

Answer(s): (a) 1 km; (b) 6.5 km