A salon and a cafe, 1500 m apart, are situated between Marion's house and Zara's house. The cafe is halfway between the two houses and the salon is closer to Zara's house. Marion and Zara left their homes at the same time and arrived at the salon at the same time. Marion drove at a speed of 68 km/h while Zara drove at a speed 10 km/h slower than Marion. Leaving your answer in kilometres,

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

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

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

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

Distance that Marion travelled
= ³₁₀ x 68
= 20.4 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Zara's house and the cafe
= 20.4 - 1.5
= 18.9 km

Answer(s): (a) 3 km; (b) 18.9 km