A pastry shop and a flower shop, 1500 m apart, are situated between Shiyun's house and Wendy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Wendy's house. Shiyun and Wendy left their homes at the same time and arrived at the pastry shop at the same time. Shiyun drove at a speed of 64 km/h while Wendy drove at a speed 10 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

Distance that Shiyun travelled more than Wendy
= 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 pastry shop
= 3 ÷ 10
= ³₁₀ h

Distance that Shiyun travelled
= ³₁₀ x 64
= 19.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Wendy's house and the flower shop
= 19.2 - 1.5
= 17.7 km

Answer(s): (a) 3 km; (b) 17.7 km