A park and a museum, 1000 m apart, are situated between Dana's house and Eva's house. The museum is halfway between the two houses and the park is closer to Eva's house. Dana and Eva left their homes at the same time and arrived at the park at the same time. Dana drove at a speed of 66 km/h while Eva drove at a speed 11 km/h slower than Dana. Leaving your answer in kilometres,

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

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

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

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

Distance that Dana travelled
= ²₁₁ x 66
= 12 km

1000 m = 1 km
1000 m = 1 km

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

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