A church and a flower shop, 500 m apart, are situated between Emily's house and Shiyun's house. The flower shop is halfway between the two houses and the church is closer to Shiyun's house. Emily and Shiyun left their homes at the same time and arrived at the church at the same time. Emily drove at a speed of 63 km/h while Shiyun drove at a speed 15 km/h slower than Emily. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emily took to travel to the church
= 1 ÷ 15
= ¹₁₅ h

Distance that Emily travelled
= ¹₁₅ x 63
= 4.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Shiyun's house and the flower shop
= 4.2 - 0.5
= 3.7 km

Answer(s): (a) 1 km; (b) 3.7 km