A park and a museum, 500 m apart, are situated between Xylia's house and Mary's house. The museum is halfway between the two houses and the park is closer to Mary's house. Xylia and Mary left their homes at the same time and arrived at the park at the same time. Xylia drove at a speed of 67 km/h while Mary drove at a speed 10 km/h slower than Xylia. Leaving your answer in kilometres,

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

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

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

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

Distance that Xylia travelled
= ¹₁₀ x 67
= 6.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Mary's house and the museum
= 6.7 - 0.5
= 6.2 km

Answer(s): (a) 1 km; (b) 6.2 km