A park and a museum, 500 m apart, are situated between Kimberly's house and Zara's house. The museum is halfway between the two houses and the park is closer to Zara's house. Kimberly and Zara left their homes at the same time and arrived at the park at the same time. Kimberly drove at a speed of 80 km/h while Zara drove at a speed 20 km/h slower than Kimberly. Leaving your answer in kilometres,

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

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

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

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

Distance that Kimberly travelled
= ¹₂₀ x 80
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Zara's house and the museum
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km