A pastry shop and a flower shop, 500 m apart, are situated between Opal's house and Dana's house. The flower shop is halfway between the two houses and the pastry shop is closer to Dana's house. Opal and Dana left their homes at the same time and arrived at the pastry shop at the same time. Opal drove at a speed of 71 km/h while Dana drove at a speed 10 km/h slower than Opal. Leaving your answer in kilometres,

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

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

Distance that Opal travelled more than Dana
= 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 71
= 7.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Dana's house and the flower shop
= 7.1 - 0.5
= 6.6 km

Answer(s): (a) 1 km; (b) 6.6 km