A pastry shop and a flower shop, 2000 m apart, are situated between Vanessa'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. Vanessa and Shannon left their homes at the same time and arrived at the pastry shop at the same time. Vanessa drove at a speed of 66 km/h while Shannon drove at a speed 15 km/h slower than Vanessa. Leaving your answer in kilometres,

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

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

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

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

Distance that Vanessa travelled
= ⁴₁₅ x 66
= 17.6 km

1000 m = 1 km
2000 m = 2 km

Distance between Shannon's house and the flower shop
= 17.6 - 2
= 15.6 km

Answer(s): (a) 4 km; (b) 15.6 km