A pastry shop and a flower shop, 500 m apart, are situated between Diana's house and Kathy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Kathy's house. Diana and Kathy left their homes at the same time and arrived at the pastry shop at the same time. Diana drove at a speed of 65 km/h while Kathy drove at a speed 10 km/h slower than Diana. Leaving your answer in kilometres,

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

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

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

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

Distance that Diana travelled
= ¹₁₀ x 65
= 6.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Kathy's house and the flower shop
= 6.5 - 0.5
= 6 km

Answer(s): (a) 1 km; (b) 6 km