A pastry shop and a flower shop, 500 m apart, are situated between Vanessa's house and Wendy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Wendy's house. Vanessa and Wendy left their homes at the same time and arrived at the pastry shop at the same time. Vanessa drove at a speed of 60 km/h while Wendy drove at a speed 12 km/h slower than Vanessa. Leaving your answer in kilometres,

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

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

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

(b)
Time that Vanessa took to travel to the pastry shop
= 1 ÷ 12
= ¹₁₂ h

Distance that Vanessa travelled
= ¹₁₂ x 60
= 5 km

1000 m = 1 km
500 m = 0.5 km

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

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