A church and a flower shop, 500 m apart, are situated between Mary's house and Shiyun's house. The flower shop is halfway between the two houses and the church is closer to Shiyun's house. Mary and Shiyun left their homes at the same time and arrived at the church at the same time. Mary drove at a speed of 68 km/h while Shiyun drove at a speed 10 km/h slower than Mary. Leaving your answer in kilometres,

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

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

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

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

Distance that Mary travelled
= ¹₁₀ x 68
= 6.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Shiyun's house and the flower shop
= 6.8 - 0.5
= 6.3 km

Answer(s): (a) 1 km; (b) 6.3 km