A church and a flower shop, 2500 m apart, are situated between Fiona's house and Hazel's house. The flower shop is halfway between the two houses and the church is closer to Hazel's house. Fiona and Hazel left their homes at the same time and arrived at the church at the same time. Fiona drove at a speed of 63 km/h while Hazel drove at a speed 18 km/h slower than Fiona. Leaving your answer in kilometres,

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

(a)
Let the distance between Fiona's house and Hazel's house be 1 d.
Hazel travelled = ¹₂ d - 2500 m
Fiona travelled = ¹₂ d + 2500 m

Distance that Fiona travelled more than Hazel
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Fiona took to travel to the church
= 5 ÷ 18
= ⁵₁₈ h

Distance that Fiona travelled
= ⁵₁₈ x 63
= 17.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Hazel's house and the flower shop
= 17.5 - 2.5
= 15 km

Answer(s): (a) 5 km; (b) 15 km