A park and a museum, 500 m apart, are situated between Min's house and Opal's house. The museum is halfway between the two houses and the park is closer to Opal's house. Min and Opal left their homes at the same time and arrived at the park at the same time. Min drove at a speed of 74 km/h while Opal drove at a speed 20 km/h slower than Min. Leaving your answer in kilometres,

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

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

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

(b)
Time that Min took to travel to the park
= 1 ÷ 20
= ¹₂₀ h

Distance that Min travelled
= ¹₂₀ x 74
= 3.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Opal's house and the museum
= 3.7 - 0.5
= 3.2 km

Answer(s): (a) 1 km; (b) 3.2 km