A church and a flower shop, 3500 m apart, are situated between Linda's house and Jen's house. The flower shop is halfway between the two houses and the church is closer to Jen's house. Linda and Jen left their homes at the same time and arrived at the church at the same time. Linda drove at a speed of 63 km/h while Jen drove at a speed 20 km/h slower than Linda. Leaving your answer in kilometres,

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

(a)
Let the distance between Linda's house and Jen's house be 1 d.
Jen travelled = ¹₂ d - 3500 m
Linda travelled = ¹₂ d + 3500 m

Distance that Linda travelled more than Jen
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Linda took to travel to the church
= 7 ÷ 20
= ⁷₂₀ h

Distance that Linda travelled
= ⁷₂₀ x 63
= 22.05 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Jen's house and the flower shop
= 22.05 - 3.5
= 18.55 km

Answer(s): (a) 7 km; (b) 18.55 km