A salon and a cafe, 1500 m apart, are situated between Olivia's house and Cindy's house. The cafe is halfway between the two houses and the salon is closer to Cindy's house. Olivia and Cindy left their homes at the same time and arrived at the salon at the same time. Olivia drove at a speed of 72 km/h while Cindy drove at a speed 16 km/h slower than Olivia. Leaving your answer in kilometres,

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

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

Distance that Olivia travelled more than Cindy
= 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 ÷ 16
= ³₁₆ h

Distance that Olivia travelled
= ³₁₆ x 72
= 13.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Cindy's house and the cafe
= 13.5 - 1.5
= 12 km

Answer(s): (a) 3 km; (b) 12 km