A church and a flower shop, 500 m apart, are situated between Raeann's house and Kylie's house. The flower shop is halfway between the two houses and the church is closer to Kylie's house. Raeann and Kylie left their homes at the same time and arrived at the church at the same time. Raeann drove at a speed of 65 km/h while Kylie drove at a speed 13 km/h slower than Raeann. Leaving your answer in kilometres,

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

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

Distance that Raeann travelled more than Kylie
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Raeann took to travel to the church
= 1 ÷ 13
= ¹₁₃ h

Distance that Raeann travelled
= ¹₁₃ x 65
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Kylie's house and the flower shop
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km