A pastry shop and a flower shop, 500 m apart, are situated between Vanessa's house and Linda's house. The flower shop is halfway between the two houses and the pastry shop is closer to Linda's house. Vanessa and Linda left their homes at the same time and arrived at the pastry shop at the same time. Vanessa drove at a speed of 77 km/h while Linda drove at a speed 10 km/h slower than Vanessa. Leaving your answer in kilometres,

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

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

Distance that Vanessa travelled more than Linda
= 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 ÷ 10
= ¹₁₀ h

Distance that Vanessa travelled
= ¹₁₀ x 77
= 7.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Linda's house and the flower shop
= 7.7 - 0.5
= 7.2 km

Answer(s): (a) 1 km; (b) 7.2 km