A salon and a cafe, 1500 m apart, are situated between Cindy's house and Xylia's house. The cafe is halfway between the two houses and the salon is closer to Xylia's house. Cindy and Xylia left their homes at the same time and arrived at the salon at the same time. Cindy drove at a speed of 79 km/h while Xylia drove at a speed 20 km/h slower than Cindy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Cindy took to travel to the salon
= 3 ÷ 20
= ³₂₀ h

Distance that Cindy travelled
= ³₂₀ x 79
= 11.85 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Xylia's house and the cafe
= 11.85 - 1.5
= 10.35 km

Answer(s): (a) 3 km; (b) 10.35 km