A salon and a cafe, 500 m apart, are situated between Lynn's house and Elyse's house. The cafe is halfway between the two houses and the salon is closer to Elyse's house. Lynn and Elyse left their homes at the same time and arrived at the salon at the same time. Lynn drove at a speed of 70 km/h while Elyse drove at a speed 20 km/h slower than Lynn. Leaving your answer in kilometres,

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

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

Distance that Lynn travelled more than Elyse
= 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 70
= 3.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Elyse's house and the cafe
= 3.5 - 0.5
= 3 km

Answer(s): (a) 1 km; (b) 3 km