A pastry shop and a flower shop, 500 m apart, are situated between Gabby's house and Nora's house. The flower shop is halfway between the two houses and the pastry shop is closer to Nora's house. Gabby and Nora left their homes at the same time and arrived at the pastry shop at the same time. Gabby drove at a speed of 76 km/h while Nora drove at a speed 19 km/h slower than Gabby. Leaving your answer in kilometres,

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

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

Distance that Gabby travelled more than Nora
= 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 ÷ 19
= ¹₁₉ h

Distance that Gabby travelled
= ¹₁₉ x 76
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Nora's house and the flower shop
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km