A church and a flower shop, 1500 m apart, are situated between Zara's house and Gwen's house. The flower shop is halfway between the two houses and the church is closer to Gwen's house. Zara and Gwen left their homes at the same time and arrived at the church at the same time. Zara drove at a speed of 63 km/h while Gwen drove at a speed 14 km/h slower than Zara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zara took to travel to the church
= 3 ÷ 14
= ³₁₄ h

Distance that Zara travelled
= ³₁₄ x 63
= 13.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Gwen's house and the flower shop
= 13.5 - 1.5
= 12 km

Answer(s): (a) 3 km; (b) 12 km