A pastry shop and a flower shop, 2000 m apart, are situated between Tiffany'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. Tiffany and Cathy left their homes at the same time and arrived at the pastry shop at the same time. Tiffany drove at a speed of 65 km/h while Cathy drove at a speed 13 km/h slower than Tiffany. Leaving your answer in kilometres,

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

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

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

(b)
Time that Tiffany took to travel to the pastry shop
= 4 ÷ 13
= ⁴₁₃ h

Distance that Tiffany travelled
= ⁴₁₃ x 65
= 20 km

1000 m = 1 km
2000 m = 2 km

Distance between Cathy's house and the flower shop
= 20 - 2
= 18 km

Answer(s): (a) 4 km; (b) 18 km