A park and a museum, 500 m apart, are situated between Mary's house and Jade's house. The museum is halfway between the two houses and the park is closer to Jade's house. Mary and Jade left their homes at the same time and arrived at the park at the same time. Mary drove at a speed of 66 km/h while Jade drove at a speed 11 km/h slower than Mary. Leaving your answer in kilometres,

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

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

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

(b)
Time that Mary took to travel to the park
= 1 ÷ 11
= ¹₁₁ h

Distance that Mary travelled
= ¹₁₁ x 66
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jade's house and the museum
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km