A church and a flower shop, 1500 m apart, are situated between Shiyun's house and Zara's house. The flower shop is halfway between the two houses and the church is closer to Zara's house. Shiyun and Zara left their homes at the same time and arrived at the church at the same time. Shiyun drove at a speed of 62 km/h while Zara drove at a speed 10 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

Distance that Shiyun travelled more than Zara
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Shiyun took to travel to the church
= 3 ÷ 10
= ³₁₀ h

Distance that Shiyun travelled
= ³₁₀ x 62
= 18.6 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Zara's house and the flower shop
= 18.6 - 1.5
= 17.1 km

Answer(s): (a) 3 km; (b) 17.1 km