A park and a museum, 500 m apart, are situated between Nicole's house and Lucy's house. The museum is halfway between the two houses and the park is closer to Lucy's house. Nicole and Lucy left their homes at the same time and arrived at the park at the same time. Nicole drove at a speed of 79 km/h while Lucy drove at a speed 20 km/h slower than Nicole. Leaving your answer in kilometres,

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

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

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

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

Distance that Nicole travelled
= ¹₂₀ x 79
= 3.95 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lucy's house and the museum
= 3.95 - 0.5
= 3.45 km

Answer(s): (a) 1 km; (b) 3.45 km