A salon and a cafe, 500 m apart, are situated between Eva's house and Kimberly's house. The cafe is halfway between the two houses and the salon is closer to Kimberly's house. Eva and Kimberly left their homes at the same time and arrived at the salon at the same time. Eva drove at a speed of 69 km/h while Kimberly drove at a speed 20 km/h slower than Eva. Leaving your answer in kilometres,

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

(a)
Let the distance between Eva's house and Kimberly's house be 1 d.
Kimberly travelled = ¹₂ d - 500 m
Eva travelled = ¹₂ d + 500 m

Distance that Eva travelled more than Kimberly
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Eva took to travel to the salon
= 1 ÷ 20
= ¹₂₀ h

Distance that Eva travelled
= ¹₂₀ x 69
= 3.45 km

1000 m = 1 km
500 m = 0.5 km

Distance between Kimberly's house and the cafe
= 3.45 - 0.5
= 2.95 km

Answer(s): (a) 1 km; (b) 2.95 km