A church and a flower shop, 2000 m apart, are situated between Zoe's house and Vanessa's house. The flower shop is halfway between the two houses and the church is closer to Vanessa's house. Zoe and Vanessa left their homes at the same time and arrived at the church at the same time. Zoe drove at a speed of 66 km/h while Vanessa drove at a speed 15 km/h slower than Zoe. Leaving your answer in kilometres,

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

(a)
Let the distance between Zoe's house and Vanessa's house be 1 d.
Vanessa travelled = ¹₂ d - 2000 m
Zoe travelled = ¹₂ d + 2000 m

Distance that Zoe travelled more than Vanessa
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Zoe took to travel to the church
= 4 ÷ 15
= ⁴₁₅ h

Distance that Zoe travelled
= ⁴₁₅ x 66
= 17.6 km

1000 m = 1 km
2000 m = 2 km

Distance between Vanessa's house and the flower shop
= 17.6 - 2
= 15.6 km

Answer(s): (a) 4 km; (b) 15.6 km