A park and a museum, 2500 m apart, are situated between Linda's house and Shannon's house. The museum is halfway between the two houses and the park is closer to Shannon's house. Linda and Shannon left their homes at the same time and arrived at the park at the same time. Linda drove at a speed of 63 km/h while Shannon drove at a speed 14 km/h slower than Linda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Linda took to travel to the park
= 5 ÷ 14
= ⁵₁₄ h

Distance that Linda travelled
= ⁵₁₄ x 63
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Shannon's house and the museum
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km