A salon and a cafe, 2000 m apart, are situated between Min's house and Gillian's house. The cafe is halfway between the two houses and the salon is closer to Gillian's house. Min and Gillian left their homes at the same time and arrived at the salon at the same time. Min drove at a speed of 75 km/h while Gillian drove at a speed 15 km/h slower than Min. Leaving your answer in kilometres,

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

(a)
Let the distance between Min's house and Gillian's house be 1 d.
Gillian travelled = ¹₂ d - 2000 m
Min travelled = ¹₂ d + 2000 m

Distance that Min travelled more than Gillian
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Min took to travel to the salon
= 4 ÷ 15
= ⁴₁₅ h

Distance that Min travelled
= ⁴₁₅ x 75
= 20 km

1000 m = 1 km
2000 m = 2 km

Distance between Gillian's house and the cafe
= 20 - 2
= 18 km

Answer(s): (a) 4 km; (b) 18 km