A salon and a cafe, 500 m apart, are situated between Cathy's house and Hilda's house. The cafe is halfway between the two houses and the salon is closer to Hilda's house. Cathy and Hilda left their homes at the same time and arrived at the salon at the same time. Cathy drove at a speed of 62 km/h while Hilda drove at a speed 20 km/h slower than Cathy. Leaving your answer in kilometres,

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

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

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

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

Distance that Cathy travelled
= ¹₂₀ x 62
= 3.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Hilda's house and the cafe
= 3.1 - 0.5
= 2.6 km

Answer(s): (a) 1 km; (b) 2.6 km