A pastry shop and a flower shop, 500 m apart, are situated between Gabby's house and Vanessa's house. The flower shop is halfway between the two houses and the pastry shop is closer to Vanessa's house. Gabby and Vanessa left their homes at the same time and arrived at the pastry shop at the same time. Gabby drove at a speed of 68 km/h while Vanessa drove at a speed 20 km/h slower than Gabby. Leaving your answer in kilometres,

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

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

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

(b)
Time that Gabby took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Gabby travelled
= ¹₂₀ x 68
= 3.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Vanessa's house and the flower shop
= 3.4 - 0.5
= 2.9 km

Answer(s): (a) 1 km; (b) 2.9 km