A park and a museum, 500 m apart, are situated between Cindy's house and Irene's house. The museum is halfway between the two houses and the park is closer to Irene's house. Cindy and Irene left their homes at the same time and arrived at the park at the same time. Cindy drove at a speed of 76 km/h while Irene drove at a speed 20 km/h slower than Cindy. Leaving your answer in kilometres,

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

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

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

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

Distance that Cindy travelled
= ¹₂₀ x 76
= 3.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Irene's house and the museum
= 3.8 - 0.5
= 3.3 km

Answer(s): (a) 1 km; (b) 3.3 km