A park and a museum, 500 m apart, are situated between Xylia's house and Xuan's house. The museum is halfway between the two houses and the park is closer to Xuan's house. Xylia and Xuan left their homes at the same time and arrived at the park at the same time. Xylia drove at a speed of 74 km/h while Xuan drove at a speed 10 km/h slower than Xylia. Leaving your answer in kilometres,

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

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

Distance that Xylia travelled more than Xuan
= 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 74
= 7.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Xuan's house and the museum
= 7.4 - 0.5
= 6.9 km

Answer(s): (a) 1 km; (b) 6.9 km