A park and a museum, 500 m apart, are situated between Betty's house and Gwen's house. The museum is halfway between the two houses and the park is closer to Gwen's house. Betty and Gwen left their homes at the same time and arrived at the park at the same time. Betty drove at a speed of 77 km/h while Gwen drove at a speed 14 km/h slower than Betty. Leaving your answer in kilometres,

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

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

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

(b)
Time that Betty took to travel to the park
= 1 ÷ 14
= ¹₁₄ h

Distance that Betty travelled
= ¹₁₄ x 77
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Gwen's house and the museum
= 5.5 - 0.5
= 5 km

Answer(s): (a) 1 km; (b) 5 km