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

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

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

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

(b)
Time that Anna took to travel to the pastry shop
= 1 ÷ 16
= ¹₁₆ h

Distance that Anna travelled
= ¹₁₆ x 64
= 4 km

1000 m = 1 km
500 m = 0.5 km

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

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