A park and a museum, 2000 m apart, are situated between Xuan's house and Opal's house. The museum is halfway between the two houses and the park is closer to Opal's house. Xuan and Opal left their homes at the same time and arrived at the park at the same time. Xuan drove at a speed of 75 km/h while Opal drove at a speed 15 km/h slower than Xuan. Leaving your answer in kilometres,

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

(a)
Let the distance between Xuan's house and Opal's house be 1 d.
Opal travelled = ¹₂ d - 2000 m
Xuan travelled = ¹₂ d + 2000 m

Distance that Xuan travelled more than Opal
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Xuan took to travel to the park
= 4 ÷ 15
= ⁴₁₅ h

Distance that Xuan travelled
= ⁴₁₅ x 75
= 20 km

1000 m = 1 km
2000 m = 2 km

Distance between Opal's house and the museum
= 20 - 2
= 18 km

Answer(s): (a) 4 km; (b) 18 km