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

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

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

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

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

Distance that Cathy travelled
= ³₂₀ x 79
= 11.85 km

1000 m = 1 km
1500 m = 1.5 km

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

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