A pastry shop and a flower shop, 2000 m apart, are situated between Sabrina'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. Sabrina and Gwen left their homes at the same time and arrived at the pastry shop at the same time. Sabrina drove at a speed of 78 km/h while Gwen drove at a speed 15 km/h slower than Sabrina. Leaving your answer in kilometres,

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

(a)
Let the distance between Sabrina's house and Gwen's house be 1 d.
Gwen travelled = ¹₂ d - 2000 m
Sabrina travelled = ¹₂ d + 2000 m

Distance that Sabrina travelled more than Gwen
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Sabrina took to travel to the pastry shop
= 4 ÷ 15
= ⁴₁₅ h

Distance that Sabrina travelled
= ⁴₁₅ x 78
= 20.8 km

1000 m = 1 km
2000 m = 2 km

Distance between Gwen's house and the flower shop
= 20.8 - 2
= 18.8 km

Answer(s): (a) 4 km; (b) 18.8 km