A pastry shop and a flower shop, 1000 m apart, are situated between Barbara's house and Lynn's house. The flower shop is halfway between the two houses and the pastry shop is closer to Lynn's house. Barbara and Lynn left their homes at the same time and arrived at the pastry shop at the same time. Barbara drove at a speed of 78 km/h while Lynn drove at a speed 15 km/h slower than Barbara. Leaving your answer in kilometres,

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

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

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

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

Distance that Barbara travelled
= ²₁₅ x 78
= 10.4 km

1000 m = 1 km
1000 m = 1 km

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

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