A salon and a cafe, 500 m apart, are situated between Lynn's house and Irene's house. The cafe is halfway between the two houses and the salon is closer to Irene's house. Lynn and Irene left their homes at the same time and arrived at the salon at the same time. Lynn drove at a speed of 63 km/h while Irene drove at a speed 20 km/h slower than Lynn. Leaving your answer in kilometres,

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

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

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

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

Distance that Lynn travelled
= ¹₂₀ x 63
= 3.15 km

1000 m = 1 km
500 m = 0.5 km

Distance between Irene's house and the cafe
= 3.15 - 0.5
= 2.65 km

Answer(s): (a) 1 km; (b) 2.65 km