A park and a museum, 500 m apart, are situated between Shannon's house and Yoko's house. The museum is halfway between the two houses and the park is closer to Yoko's house. Shannon and Yoko left their homes at the same time and arrived at the park at the same time. Shannon drove at a speed of 60 km/h while Yoko drove at a speed 20 km/h slower than Shannon. Leaving your answer in kilometres,

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

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

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

(b)
Time that Shannon took to travel to the park
= 1 ÷ 20
= ¹₂₀ h

Distance that Shannon travelled
= ¹₂₀ x 60
= 3 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yoko's house and the museum
= 3 - 0.5
= 2.5 km

Answer(s): (a) 1 km; (b) 2.5 km