A salon and a cafe, 500 m apart, are situated between Hilda's house and Shannon's house. The cafe is halfway between the two houses and the salon is closer to Shannon's house. Hilda and Shannon left their homes at the same time and arrived at the salon at the same time. Hilda drove at a speed of 62 km/h while Shannon drove at a speed 10 km/h slower than Hilda. Leaving your answer in kilometres,

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

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

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

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

Distance that Hilda travelled
= ¹₁₀ x 62
= 6.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Shannon's house and the cafe
= 6.2 - 0.5
= 5.7 km

Answer(s): (a) 1 km; (b) 5.7 km