A park and a museum, 1500 m apart, are situated between Marion's house and Anna's house. The museum is halfway between the two houses and the park is closer to Anna's house. Marion and Anna left their homes at the same time and arrived at the park at the same time. Marion drove at a speed of 66 km/h while Anna drove at a speed 10 km/h slower than Marion. Leaving your answer in kilometres,

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

(a)
Let the distance between Marion's house and Anna's house be 1 d.
Anna travelled = ¹₂ d - 1500 m
Marion travelled = ¹₂ d + 1500 m

Distance that Marion travelled more than Anna
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Marion took to travel to the park
= 3 ÷ 10
= ³₁₀ h

Distance that Marion travelled
= ³₁₀ x 66
= 19.8 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Anna's house and the museum
= 19.8 - 1.5
= 18.3 km

Answer(s): (a) 3 km; (b) 18.3 km