A salon and a cafe, 500 m apart, are situated between Gillian's house and Kimberly's house. The cafe is halfway between the two houses and the salon is closer to Kimberly's house. Gillian and Kimberly left their homes at the same time and arrived at the salon at the same time. Gillian drove at a speed of 80 km/h while Kimberly drove at a speed 20 km/h slower than Gillian. Leaving your answer in kilometres,

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

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

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

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

Distance that Gillian travelled
= ¹₂₀ x 80
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Kimberly's house and the cafe
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km