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

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

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

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

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

Distance that Jean travelled
= ⁵₁₉ x 76
= 20 km

1000 m = 1 km
2500 m = 2.5 km

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

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