A salon and a cafe, 3500 m apart, are situated between Natalie's house and Marion's house. The cafe is halfway between the two houses and the salon is closer to Marion's house. Natalie and Marion left their homes at the same time and arrived at the salon at the same time. Natalie drove at a speed of 61 km/h while Marion drove at a speed 20 km/h slower than Natalie. Leaving your answer in kilometres,

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

(a)
Let the distance between Natalie's house and Marion's house be 1 d.
Marion travelled = ¹₂ d - 3500 m
Natalie travelled = ¹₂ d + 3500 m

Distance that Natalie travelled more than Marion
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Natalie took to travel to the salon
= 7 ÷ 20
= ⁷₂₀ h

Distance that Natalie travelled
= ⁷₂₀ x 61
= 21.35 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Marion's house and the cafe
= 21.35 - 3.5
= 17.85 km

Answer(s): (a) 7 km; (b) 17.85 km