A pastry shop and a flower shop, 1500 m apart, are situated between Emma'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. Emma and Shannon left their homes at the same time and arrived at the pastry shop at the same time. Emma drove at a speed of 60 km/h while Shannon drove at a speed 20 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the pastry shop
= 3 ÷ 20
= ³₂₀ h

Distance that Emma travelled
= ³₂₀ x 60
= 9 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Shannon's house and the flower shop
= 9 - 1.5
= 7.5 km

Answer(s): (a) 3 km; (b) 7.5 km