A pastry shop and a flower shop, 500 m apart, are situated between Barbara's house and Emily's house. The flower shop is halfway between the two houses and the pastry shop is closer to Emily's house. Barbara and Emily left their homes at the same time and arrived at the pastry shop at the same time. Barbara drove at a speed of 66 km/h while Emily drove at a speed 15 km/h slower than Barbara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Barbara took to travel to the pastry shop
= 1 ÷ 15
= ¹₁₅ h

Distance that Barbara travelled
= ¹₁₅ x 66
= 4.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Emily's house and the flower shop
= 4.4 - 0.5
= 3.9 km

Answer(s): (a) 1 km; (b) 3.9 km