A church and a flower shop, 1500 m apart, are situated between Zara's house and Yoko's house. The flower shop is halfway between the two houses and the church is closer to Yoko's house. Zara and Yoko left their homes at the same time and arrived at the church at the same time. Zara drove at a speed of 64 km/h while Yoko drove at a speed 20 km/h slower than Zara. Leaving your answer in kilometres,

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

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

Distance that Zara travelled more than Yoko
= 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 ÷ 20
= ³₂₀ h

Distance that Zara travelled
= ³₂₀ x 64
= 9.6 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Yoko's house and the flower shop
= 9.6 - 1.5
= 8.1 km

Answer(s): (a) 3 km; (b) 8.1 km