A park and a museum, 500 m apart, are situated between Jean's house and Roshel's house. The museum is halfway between the two houses and the park is closer to Roshel's house. Jean and Roshel left their homes at the same time and arrived at the park at the same time. Jean drove at a speed of 77 km/h while Roshel drove at a speed 20 km/h slower than Jean. Leaving your answer in kilometres,

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

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

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

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

Distance that Jean travelled
= ¹₂₀ x 77
= 3.85 km

1000 m = 1 km
500 m = 0.5 km

Distance between Roshel's house and the museum
= 3.85 - 0.5
= 3.35 km

Answer(s): (a) 1 km; (b) 3.35 km