A salon and a cafe, 500 m apart, are situated between Mary's house and Nora's house. The cafe is halfway between the two houses and the salon is closer to Nora's house. Mary and Nora left their homes at the same time and arrived at the salon at the same time. Mary drove at a speed of 80 km/h while Nora drove at a speed 20 km/h slower than Mary. Leaving your answer in kilometres,

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

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

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

(b)
Time that Mary took to travel to the salon
= 1 ÷ 20
= ¹₂₀ h

Distance that Mary travelled
= ¹₂₀ x 80
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Nora's house and the cafe
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km