A pastry shop and a flower shop, 500 m apart, are situated between Erika's house and Sarah's house. The flower shop is halfway between the two houses and the pastry shop is closer to Sarah's house. Erika and Sarah left their homes at the same time and arrived at the pastry shop at the same time. Erika drove at a speed of 80 km/h while Sarah drove at a speed 16 km/h slower than Erika. Leaving your answer in kilometres,

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

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

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

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

Distance that Erika travelled
= ¹₁₆ x 80
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Sarah's house and the flower shop
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km