A park and a museum, 1000 m apart, are situated between Marion's house and Gillian's house. The museum is halfway between the two houses and the park is closer to Gillian's house. Marion and Gillian 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 Gillian drove at a speed 11 km/h slower than Marion. Leaving your answer in kilometres,

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

(a)
Let the distance between Marion's house and Gillian's house be 1 d.
Gillian travelled = ¹₂ d - 1000 m
Marion travelled = ¹₂ d + 1000 m

Distance that Marion travelled more than Gillian
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Marion took to travel to the park
= 2 ÷ 11
= ²₁₁ h

Distance that Marion travelled
= ²₁₁ x 66
= 12 km

1000 m = 1 km
1000 m = 1 km

Distance between Gillian's house and the museum
= 12 - 1
= 11 km

Answer(s): (a) 2 km; (b) 11 km