A pastry shop and a flower shop, 1000 m apart, are situated between Eva's house and Gabby's house. The flower shop is halfway between the two houses and the pastry shop is closer to Gabby's house. Eva and Gabby left their homes at the same time and arrived at the pastry shop at the same time. Eva drove at a speed of 65 km/h while Gabby drove at a speed 13 km/h slower than Eva. Leaving your answer in kilometres,

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

(a)
Let the distance between Eva's house and Gabby's house be 1 d.
Gabby travelled = ¹₂ d - 1000 m
Eva travelled = ¹₂ d + 1000 m

Distance that Eva travelled more than Gabby
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Eva took to travel to the pastry shop
= 2 ÷ 13
= ²₁₃ h

Distance that Eva travelled
= ²₁₃ x 65
= 10 km

1000 m = 1 km
1000 m = 1 km

Distance between Gabby's house and the flower shop
= 10 - 1
= 9 km

Answer(s): (a) 2 km; (b) 9 km