A church and a flower shop, 1500 m apart, are situated between Tina's house and Cindy's house. The flower shop is halfway between the two houses and the church is closer to Cindy's house. Tina and Cindy left their homes at the same time and arrived at the church at the same time. Tina drove at a speed of 80 km/h while Cindy drove at a speed 20 km/h slower than Tina. Leaving your answer in kilometres,

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

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

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

(b)
Time that Tina took to travel to the church
= 3 ÷ 20
= ³₂₀ h

Distance that Tina travelled
= ³₂₀ x 80
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Cindy's house and the flower shop
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km