A pastry shop and a flower shop, 1500 m apart, are situated between Wendy'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. Wendy and Kathy left their homes at the same time and arrived at the pastry shop at the same time. Wendy drove at a speed of 69 km/h while Kathy drove at a speed 20 km/h slower than Wendy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Wendy took to travel to the pastry shop
= 3 ÷ 20
= ³₂₀ h

Distance that Wendy travelled
= ³₂₀ x 69
= 10.35 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kathy's house and the flower shop
= 10.35 - 1.5
= 8.85 km

Answer(s): (a) 3 km; (b) 8.85 km