A church and a flower shop, 500 m apart, are situated between Shiyun's house and Hazel's house. The flower shop is halfway between the two houses and the church is closer to Hazel's house. Shiyun and Hazel left their homes at the same time and arrived at the church at the same time. Shiyun drove at a speed of 64 km/h while Hazel drove at a speed 10 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

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

(b)
Time that Shiyun took to travel to the church
= 1 ÷ 10
= ¹₁₀ h

Distance that Shiyun travelled
= ¹₁₀ x 64
= 6.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Hazel's house and the flower shop
= 6.4 - 0.5
= 5.9 km

Answer(s): (a) 1 km; (b) 5.9 km