A pastry shop and a flower shop, 500 m apart, are situated between Emma's house and Opal's house. The flower shop is halfway between the two houses and the pastry shop is closer to Opal's house. Emma and Opal left their homes at the same time and arrived at the pastry shop at the same time. Emma drove at a speed of 74 km/h while Opal drove at a speed 10 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

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

Distance that Emma travelled
= ¹₁₀ x 74
= 7.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Opal's house and the flower shop
= 7.4 - 0.5
= 6.9 km

Answer(s): (a) 1 km; (b) 6.9 km