A pastry shop and a flower shop, 2000 m apart, are situated between Xuan's house and Shannon's house. The flower shop is halfway between the two houses and the pastry shop is closer to Shannon's house. Xuan and Shannon left their homes at the same time and arrived at the pastry shop at the same time. Xuan drove at a speed of 69 km/h while Shannon drove at a speed 15 km/h slower than Xuan. Leaving your answer in kilometres,

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

(a)
Let the distance between Xuan's house and Shannon's house be 1 d.
Shannon travelled = ¹₂ d - 2000 m
Xuan travelled = ¹₂ d + 2000 m

Distance that Xuan travelled more than Shannon
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Xuan took to travel to the pastry shop
= 4 ÷ 15
= ⁴₁₅ h

Distance that Xuan travelled
= ⁴₁₅ x 69
= 18.4 km

1000 m = 1 km
2000 m = 2 km

Distance between Shannon's house and the flower shop
= 18.4 - 2
= 16.4 km

Answer(s): (a) 4 km; (b) 16.4 km