A pastry shop and a flower shop, 1500 m apart, are situated between Gabby's house and Fanny's house. The flower shop is halfway between the two houses and the pastry shop is closer to Fanny's house. Gabby and Fanny 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 Fanny drove at a speed 17 km/h slower than Gabby. Leaving your answer in kilometres,

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

(a)
Let the distance between Gabby's house and Fanny's house be 1 d.
Fanny travelled = ¹₂ d - 1500 m
Gabby travelled = ¹₂ d + 1500 m

Distance that Gabby travelled more than Fanny
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Gabby took to travel to the pastry shop
= 3 ÷ 17
= ³₁₇ h

Distance that Gabby travelled
= ³₁₇ x 68
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Fanny's house and the flower shop
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km