A salon and a cafe, 3500 m apart, are situated between Gillian's house and Winnie's house. The cafe is halfway between the two houses and the salon is closer to Winnie's house. Gillian and Winnie left their homes at the same time and arrived at the salon at the same time. Gillian drove at a speed of 67 km/h while Winnie drove at a speed 20 km/h slower than Gillian. Leaving your answer in kilometres,

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

(a)
Let the distance between Gillian's house and Winnie's house be 1 d.
Winnie travelled = ¹₂ d - 3500 m
Gillian travelled = ¹₂ d + 3500 m

Distance that Gillian travelled more than Winnie
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Gillian took to travel to the salon
= 7 ÷ 20
= ⁷₂₀ h

Distance that Gillian travelled
= ⁷₂₀ x 67
= 23.45 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Winnie's house and the cafe
= 23.45 - 3.5
= 19.95 km

Answer(s): (a) 7 km; (b) 19.95 km