A park and a museum, 500 m apart, are situated between Irene's house and Sabrina's house. The museum is halfway between the two houses and the park is closer to Sabrina's house. Irene and Sabrina left their homes at the same time and arrived at the park at the same time. Irene drove at a speed of 60 km/h while Sabrina drove at a speed 10 km/h slower than Irene. Leaving your answer in kilometres,

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

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

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

(b)
Time that Irene took to travel to the park
= 1 ÷ 10
= ¹₁₀ h

Distance that Irene travelled
= ¹₁₀ x 60
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Sabrina's house and the museum
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km