A salon and a cafe, 1500 m apart, are situated between Olivia's house and Min's house. The cafe is halfway between the two houses and the salon is closer to Min's house. Olivia and Min left their homes at the same time and arrived at the salon at the same time. Olivia drove at a speed of 66 km/h while Min drove at a speed 11 km/h slower than Olivia. Leaving your answer in kilometres,

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

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

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

(b)
Time that Olivia took to travel to the salon
= 3 ÷ 11
= ³₁₁ h

Distance that Olivia travelled
= ³₁₁ x 66
= 18 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Min's house and the cafe
= 18 - 1.5
= 16.5 km

Answer(s): (a) 3 km; (b) 16.5 km