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

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

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

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

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

Distance that Vanessa travelled
= ³₁₀ x 68
= 20.4 km

1000 m = 1 km
1500 m = 1.5 km

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

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