A church and a flower shop, 1500 m apart, are situated between Linda's house and Cindy's house. The flower shop is halfway between the two houses and the church is closer to Cindy's house. Linda and Cindy left their homes at the same time and arrived at the church at the same time. Linda drove at a speed of 60 km/h while Cindy drove at a speed 16 km/h slower than Linda. Leaving your answer in kilometres,

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

(a)
Let the distance between Linda's house and Cindy's house be 1 d.
Cindy travelled = ¹₂ d - 1500 m
Linda travelled = ¹₂ d + 1500 m

Distance that Linda travelled more than Cindy
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Linda took to travel to the church
= 3 ÷ 16
= ³₁₆ h

Distance that Linda travelled
= ³₁₆ x 60
= 11.25 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Cindy's house and the flower shop
= 11.25 - 1.5
= 9.75 km

Answer(s): (a) 3 km; (b) 9.75 km