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

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

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

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

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

Distance that Natalie travelled
= ⁴₁₅ x 66
= 17.6 km

1000 m = 1 km
2000 m = 2 km

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

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