A pastry shop and a flower shop, 1500 m apart, are situated between Jane's house and Barbara's house. The flower shop is halfway between the two houses and the pastry shop is closer to Barbara's house. Jane and Barbara left their homes at the same time and arrived at the pastry shop at the same time. Jane drove at a speed of 68 km/h while Barbara drove at a speed 10 km/h slower than Jane. Leaving your answer in kilometres,

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

(a)
Let the distance between Jane's house and Barbara's house be 1 d.
Barbara travelled = ¹₂ d - 1500 m
Jane travelled = ¹₂ d + 1500 m

Distance that Jane travelled more than Barbara
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Jane took to travel to the pastry shop
= 3 ÷ 10
= ³₁₀ h

Distance that Jane travelled
= ³₁₀ x 68
= 20.4 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Barbara's house and the flower shop
= 20.4 - 1.5
= 18.9 km

Answer(s): (a) 3 km; (b) 18.9 km