A salon and a cafe, 500 m apart, are situated between Dana's house and Victoria's house. The cafe is halfway between the two houses and the salon is closer to Victoria's house. Dana and Victoria left their homes at the same time and arrived at the salon at the same time. Dana drove at a speed of 60 km/h while Victoria drove at a speed 12 km/h slower than Dana. Leaving your answer in kilometres,

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

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

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

(b)
Time that Dana took to travel to the salon
= 1 ÷ 12
= ¹₁₂ h

Distance that Dana travelled
= ¹₁₂ x 60
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Victoria's house and the cafe
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km