A park and a museum, 500 m apart, are situated between Tiffany's house and Jean's house. The museum is halfway between the two houses and the park is closer to Jean's house. Tiffany and Jean left their homes at the same time and arrived at the park at the same time. Tiffany drove at a speed of 69 km/h while Jean drove at a speed 20 km/h slower than Tiffany. Leaving your answer in kilometres,

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

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

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

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

Distance that Tiffany travelled
= ¹₂₀ x 69
= 3.45 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jean's house and the museum
= 3.45 - 0.5
= 2.95 km

Answer(s): (a) 1 km; (b) 2.95 km