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

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

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

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

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

Distance that Linda travelled
= ¹₁₄ x 77
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

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

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