A park and a museum, 500 m apart, are situated between Nora's house and Tiffany's house. The museum is halfway between the two houses and the park is closer to Tiffany's house. Nora and Tiffany left their homes at the same time and arrived at the park at the same time. Nora drove at a speed of 72 km/h while Tiffany drove at a speed 20 km/h slower than Nora. Leaving your answer in kilometres,

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

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

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

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

Distance that Nora travelled
= ¹₂₀ x 72
= 3.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Tiffany's house and the museum
= 3.6 - 0.5
= 3.1 km

Answer(s): (a) 1 km; (b) 3.1 km