A park and a museum, 500 m apart, are situated between Linda's house and Lucy's house. The museum is halfway between the two houses and the park is closer to Lucy's house. Linda and Lucy left their homes at the same time and arrived at the park at the same time. Linda drove at a speed of 61 km/h while Lucy drove at a speed 10 km/h slower than Linda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Linda took to travel to the park
= 1 ÷ 10
= ¹₁₀ h

Distance that Linda travelled
= ¹₁₀ x 61
= 6.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lucy's house and the museum
= 6.1 - 0.5
= 5.6 km

Answer(s): (a) 1 km; (b) 5.6 km