A pastry shop and a flower shop, 500 m apart, are situated between Kathy's house and Yen's house. The flower shop is halfway between the two houses and the pastry shop is closer to Yen's house. Kathy and Yen left their homes at the same time and arrived at the pastry shop at the same time. Kathy drove at a speed of 64 km/h while Yen drove at a speed 16 km/h slower than Kathy. Leaving your answer in kilometres,

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

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

Distance that Kathy travelled more than Yen
= 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 ÷ 16
= ¹₁₆ h

Distance that Kathy travelled
= ¹₁₆ x 64
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yen's house and the flower shop
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km