A pastry shop and a flower shop, 1000 m apart, are situated between Shannon'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. Shannon and Irene left their homes at the same time and arrived at the pastry shop at the same time. Shannon drove at a speed of 77 km/h while Irene drove at a speed 11 km/h slower than Shannon. Leaving your answer in kilometres,

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

(a)
Let the distance between Shannon's house and Irene's house be 1 d.
Irene travelled = ¹₂ d - 1000 m
Shannon travelled = ¹₂ d + 1000 m

Distance that Shannon travelled more than Irene
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Shannon took to travel to the pastry shop
= 2 ÷ 11
= ²₁₁ h

Distance that Shannon travelled
= ²₁₁ x 77
= 14 km

1000 m = 1 km
1000 m = 1 km

Distance between Irene's house and the flower shop
= 14 - 1
= 13 km

Answer(s): (a) 2 km; (b) 13 km