A pastry shop and a flower shop, 1500 m apart, are situated between Irene's house and Marion's house. The flower shop is halfway between the two houses and the pastry shop is closer to Marion's house. Irene and Marion left their homes at the same time and arrived at the pastry shop at the same time. Irene drove at a speed of 76 km/h while Marion drove at a speed 20 km/h slower than Irene. Leaving your answer in kilometres,

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

(a)
Let the distance between Irene's house and Marion's house be 1 d.
Marion travelled = ¹₂ d - 1500 m
Irene travelled = ¹₂ d + 1500 m

Distance that Irene travelled more than Marion
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Irene took to travel to the pastry shop
= 3 ÷ 20
= ³₂₀ h

Distance that Irene travelled
= ³₂₀ x 76
= 11.4 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Marion's house and the flower shop
= 11.4 - 1.5
= 9.9 km

Answer(s): (a) 3 km; (b) 9.9 km