A salon and a cafe, 500 m apart, are situated between Hazel's house and Elyse's house. The cafe is halfway between the two houses and the salon is closer to Elyse's house. Hazel and Elyse left their homes at the same time and arrived at the salon at the same time. Hazel drove at a speed of 68 km/h while Elyse drove at a speed 10 km/h slower than Hazel. Leaving your answer in kilometres,

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

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

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

(b)
Time that Hazel took to travel to the salon
= 1 ÷ 10
= ¹₁₀ h

Distance that Hazel travelled
= ¹₁₀ x 68
= 6.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Elyse's house and the cafe
= 6.8 - 0.5
= 6.3 km

Answer(s): (a) 1 km; (b) 6.3 km