A park and a museum, 1500 m apart, are situated between Sabrina's house and Kimberly's house. The museum is halfway between the two houses and the park is closer to Kimberly's house. Sabrina and Kimberly left their homes at the same time and arrived at the park at the same time. Sabrina drove at a speed of 77 km/h while Kimberly drove at a speed 14 km/h slower than Sabrina. Leaving your answer in kilometres,

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

(a)
Let the distance between Sabrina's house and Kimberly's house be 1 d.
Kimberly travelled = ¹₂ d - 1500 m
Sabrina travelled = ¹₂ d + 1500 m

Distance that Sabrina travelled more than Kimberly
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Sabrina took to travel to the park
= 3 ÷ 14
= ³₁₄ h

Distance that Sabrina travelled
= ³₁₄ x 77
= 16.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kimberly's house and the museum
= 16.5 - 1.5
= 15 km

Answer(s): (a) 3 km; (b) 15 km