A pastry shop and a flower shop, 500 m apart, are situated between Kathy's house and Sabrina's house. The flower shop is halfway between the two houses and the pastry shop is closer to Sabrina's house. Kathy and Sabrina left their homes at the same time and arrived at the pastry shop at the same time. Kathy drove at a speed of 71 km/h while Sabrina drove at a speed 10 km/h slower than Kathy. Leaving your answer in kilometres,

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

(a)
Let the distance between Kathy's house and Sabrina's house be 1 d.
Sabrina travelled = ¹₂ d - 500 m
Kathy travelled = ¹₂ d + 500 m

Distance that Kathy travelled more than Sabrina
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Kathy took to travel to the pastry shop
= 1 ÷ 10
= ¹₁₀ h

Distance that Kathy travelled
= ¹₁₀ x 71
= 7.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Sabrina's house and the flower shop
= 7.1 - 0.5
= 6.6 km

Answer(s): (a) 1 km; (b) 6.6 km