A church and a flower shop, 500 m apart, are situated between Zara's house and Abi's house. The flower shop is halfway between the two houses and the church is closer to Abi's house. Zara and Abi left their homes at the same time and arrived at the church at the same time. Zara drove at a speed of 78 km/h while Abi drove at a speed 13 km/h slower than Zara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zara took to travel to the church
= 1 ÷ 13
= ¹₁₃ h

Distance that Zara travelled
= ¹₁₃ x 78
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Abi's house and the flower shop
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km