A pastry shop and a flower shop, 1500 m apart, are situated between Marion's house and Gwen's house. The flower shop is halfway between the two houses and the pastry shop is closer to Gwen's house. Marion and Gwen left their homes at the same time and arrived at the pastry shop at the same time. Marion drove at a speed of 68 km/h while Gwen drove at a speed 16 km/h slower than Marion. Leaving your answer in kilometres,

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

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

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

(b)
Time that Marion took to travel to the pastry shop
= 3 ÷ 16
= ³₁₆ h

Distance that Marion travelled
= ³₁₆ x 68
= 12.75 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Gwen's house and the flower shop
= 12.75 - 1.5
= 11.25 km

Answer(s): (a) 3 km; (b) 11.25 km