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

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

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

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

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

Distance that Roshel travelled
= ¹₁₀ x 74
= 7.4 km

1000 m = 1 km
500 m = 0.5 km

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

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