A pastry shop and a flower shop, 2500 m apart, are situated between Shiyun's house and Irene's house. The flower shop is halfway between the two houses and the pastry shop is closer to Irene's house. Shiyun and Irene 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 Irene drove at a speed 16 km/h slower than Shiyun. Leaving your answer in kilometres,

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

(a)
Let the distance between Shiyun's house and Irene's house be 1 d.
Irene travelled = ¹₂ d - 2500 m
Shiyun travelled = ¹₂ d + 2500 m

Distance that Shiyun travelled more than Irene
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Shiyun took to travel to the pastry shop
= 5 ÷ 16
= ⁵₁₆ h

Distance that Shiyun travelled
= ⁵₁₆ x 64
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Irene's house and the flower shop
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km