A park and a museum, 1500 m apart, are situated between Emma's house and Tiffany's house. The museum is halfway between the two houses and the park is closer to Tiffany's house. Emma and Tiffany left their homes at the same time and arrived at the park at the same time. Emma drove at a speed of 75 km/h while Tiffany drove at a speed 20 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the park
= 3 ÷ 20
= ³₂₀ h

Distance that Emma travelled
= ³₂₀ x 75
= 11.25 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Tiffany's house and the museum
= 11.25 - 1.5
= 9.75 km

Answer(s): (a) 3 km; (b) 9.75 km