A pastry shop and a flower shop, 500 m apart, are situated between Vanessa's house and Hazel's house. The flower shop is halfway between the two houses and the pastry shop is closer to Hazel's house. Vanessa and Hazel left their homes at the same time and arrived at the pastry shop at the same time. Vanessa drove at a speed of 75 km/h while Hazel drove at a speed 20 km/h slower than Vanessa. Leaving your answer in kilometres,

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

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

Distance that Vanessa travelled more than Hazel
= 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 ÷ 20
= ¹₂₀ h

Distance that Vanessa travelled
= ¹₂₀ x 75
= 3.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Hazel's house and the flower shop
= 3.75 - 0.5
= 3.25 km

Answer(s): (a) 1 km; (b) 3.25 km