A park and a museum, 1500 m apart, are situated between Min's house and Kylie's house. The museum is halfway between the two houses and the park is closer to Kylie's house. Min and Kylie left their homes at the same time and arrived at the park at the same time. Min drove at a speed of 72 km/h while Kylie drove at a speed 16 km/h slower than Min. Leaving your answer in kilometres,

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

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

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

(b)
Time that Min took to travel to the park
= 3 ÷ 16
= ³₁₆ h

Distance that Min travelled
= ³₁₆ x 72
= 13.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kylie's house and the museum
= 13.5 - 1.5
= 12 km

Answer(s): (a) 3 km; (b) 12 km