A salon and a cafe, 500 m apart, are situated between Hilda's house and Natalie's house. The cafe is halfway between the two houses and the salon is closer to Natalie's house. Hilda and Natalie left their homes at the same time and arrived at the salon at the same time. Hilda drove at a speed of 80 km/h while Natalie drove at a speed 10 km/h slower than Hilda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Hilda took to travel to the salon
= 1 ÷ 10
= ¹₁₀ h

Distance that Hilda travelled
= ¹₁₀ x 80
= 8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Natalie's house and the cafe
= 8 - 0.5
= 7.5 km

Answer(s): (a) 1 km; (b) 7.5 km