A park and a museum, 500 m apart, are situated between Barbara's house and Linda's house. The museum is halfway between the two houses and the park is closer to Linda's house. Barbara and Linda left their homes at the same time and arrived at the park at the same time. Barbara drove at a speed of 63 km/h while Linda drove at a speed 15 km/h slower than Barbara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Barbara took to travel to the park
= 1 ÷ 15
= ¹₁₅ h

Distance that Barbara travelled
= ¹₁₅ x 63
= 4.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Linda's house and the museum
= 4.2 - 0.5
= 3.7 km

Answer(s): (a) 1 km; (b) 3.7 km