A church and a flower shop, 500 m apart, are situated between Linda's house and Irene's house. The flower shop is halfway between the two houses and the church is closer to Irene's house. Linda and Irene left their homes at the same time and arrived at the church at the same time. Linda drove at a speed of 75 km/h while Irene drove at a speed 15 km/h slower than Linda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Linda took to travel to the church
= 1 ÷ 15
= ¹₁₅ h

Distance that Linda travelled
= ¹₁₅ x 75
= 5 km

1000 m = 1 km
500 m = 0.5 km

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

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