A park and a museum, 500 m apart, are situated between Emily's house and Yoko's house. The museum is halfway between the two houses and the park is closer to Yoko's house. Emily and Yoko left their homes at the same time and arrived at the park at the same time. Emily drove at a speed of 73 km/h while Yoko drove at a speed 20 km/h slower than Emily. Leaving your answer in kilometres,

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

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

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

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

Distance that Emily travelled
= ¹₂₀ x 73
= 3.65 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yoko's house and the museum
= 3.65 - 0.5
= 3.15 km

Answer(s): (a) 1 km; (b) 3.15 km