A pastry shop and a flower shop, 1000 m apart, are situated between Emily'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. Emily and Cathy left their homes at the same time and arrived at the pastry shop at the same time. Emily drove at a speed of 78 km/h while Cathy drove at a speed 15 km/h slower than Emily. Leaving your answer in kilometres,

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

(a)
Let the distance between Emily's house and Cathy's house be 1 d.
Cathy travelled = ¹₂ d - 1000 m
Emily travelled = ¹₂ d + 1000 m

Distance that Emily travelled more than Cathy
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Emily took to travel to the pastry shop
= 2 ÷ 15
= ²₁₅ h

Distance that Emily travelled
= ²₁₅ x 78
= 10.4 km

1000 m = 1 km
1000 m = 1 km

Distance between Cathy's house and the flower shop
= 10.4 - 1
= 9.4 km

Answer(s): (a) 2 km; (b) 9.4 km