A pastry shop and a flower shop, 1500 m apart, are situated between Lucy's house and Cathy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Cathy's house. Lucy and Cathy left their homes at the same time and arrived at the pastry shop at the same time. Lucy drove at a speed of 77 km/h while Cathy drove at a speed 11 km/h slower than Lucy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Lucy took to travel to the pastry shop
= 3 ÷ 11
= ³₁₁ h

Distance that Lucy travelled
= ³₁₁ x 77
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Cathy's house and the flower shop
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km