A park and a museum, 1500 m apart, are situated between Xylia's house and Kathy's house. The museum is halfway between the two houses and the park is closer to Kathy's house. Xylia and Kathy left their homes at the same time and arrived at the park at the same time. Xylia drove at a speed of 68 km/h while Kathy drove at a speed 20 km/h slower than Xylia. Leaving your answer in kilometres,

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

(a)
Let the distance between Xylia's house and Kathy's house be 1 d.
Kathy travelled = ¹₂ d - 1500 m
Xylia travelled = ¹₂ d + 1500 m

Distance that Xylia travelled more than Kathy
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Xylia took to travel to the park
= 3 ÷ 20
= ³₂₀ h

Distance that Xylia travelled
= ³₂₀ x 68
= 10.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kathy's house and the museum
= 10.2 - 1.5
= 8.7 km

Answer(s): (a) 3 km; (b) 8.7 km