A pastry shop and a flower shop, 500 m apart, are situated between Opal's house and Tiffany's house. The flower shop is halfway between the two houses and the pastry shop is closer to Tiffany's house. Opal and Tiffany left their homes at the same time and arrived at the pastry shop at the same time. Opal drove at a speed of 75 km/h while Tiffany drove at a speed 10 km/h slower than Opal. Leaving your answer in kilometres,

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

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

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

(b)
Time that Opal took to travel to the pastry shop
= 1 ÷ 10
= ¹₁₀ h

Distance that Opal travelled
= ¹₁₀ x 75
= 7.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Tiffany's house and the flower shop
= 7.5 - 0.5
= 7 km

Answer(s): (a) 1 km; (b) 7 km