A salon and a cafe, 1500 m apart, are situated between Nora's house and Gwen's house. The cafe is halfway between the two houses and the salon is closer to Gwen's house. Nora and Gwen left their homes at the same time and arrived at the salon at the same time. Nora drove at a speed of 70 km/h while Gwen drove at a speed 10 km/h slower than Nora. Leaving your answer in kilometres,

1. how much farther did Nora travel than Gwen?
2. how far is Gwen's house from the cafe?

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

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

(b)
Time that Nora took to travel to the salon
= 3 ÷ 10
= ³₁₀ h

Distance that Nora travelled
= ³₁₀ x 70
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Gwen's house and the cafe
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km