A park and a museum, 2500 m apart, are situated between Fanny's house and Dana's house. The museum is halfway between the two houses and the park is closer to Dana's house. Fanny and Dana left their homes at the same time and arrived at the park at the same time. Fanny drove at a speed of 76 km/h while Dana drove at a speed 19 km/h slower than Fanny. Leaving your answer in kilometres,

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

(a)
Let the distance between Fanny's house and Dana's house be 1 d.
Dana travelled = ¹₂ d - 2500 m
Fanny travelled = ¹₂ d + 2500 m

Distance that Fanny travelled more than Dana
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Fanny took to travel to the park
= 5 ÷ 19
= ⁵₁₉ h

Distance that Fanny travelled
= ⁵₁₉ x 76
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Dana's house and the museum
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km