A salon and a cafe, 500 m apart, are situated between Hazel's house and Mary's house. The cafe is halfway between the two houses and the salon is closer to Mary's house. Hazel and Mary left their homes at the same time and arrived at the salon at the same time. Hazel drove at a speed of 69 km/h while Mary drove at a speed 15 km/h slower than Hazel. Leaving your answer in kilometres,

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

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

Distance that Hazel travelled more than Mary
= 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 ÷ 15
= ¹₁₅ h

Distance that Hazel travelled
= ¹₁₅ x 69
= 4.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Mary's house and the cafe
= 4.6 - 0.5
= 4.1 km

Answer(s): (a) 1 km; (b) 4.1 km