A salon and a cafe, 500 m apart, are situated between Lynn's house and Fanny's house. The cafe is halfway between the two houses and the salon is closer to Fanny's house. Lynn and Fanny left their homes at the same time and arrived at the salon at the same time. Lynn drove at a speed of 65 km/h while Fanny drove at a speed 13 km/h slower than Lynn. Leaving your answer in kilometres,

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

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

Distance that Lynn travelled more than Fanny
= 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 ÷ 13
= ¹₁₃ h

Distance that Lynn travelled
= ¹₁₃ x 65
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Fanny's house and the cafe
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km