A church and a flower shop, 500 m apart, are situated between Eva's house and Jean's house. The flower shop is halfway between the two houses and the church is closer to Jean's house. Eva and Jean left their homes at the same time and arrived at the church at the same time. Eva drove at a speed of 69 km/h while Jean drove at a speed 15 km/h slower than Eva. Leaving your answer in kilometres,

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

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

Distance that Eva travelled more than Jean
= 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 ÷ 15
= ¹₁₅ h

Distance that Eva travelled
= ¹₁₅ x 69
= 4.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jean's house and the flower shop
= 4.6 - 0.5
= 4.1 km

Answer(s): (a) 1 km; (b) 4.1 km