A park and a museum, 2000 m apart, are situated between Sabrina's house and Ivory's house. The museum is halfway between the two houses and the park is closer to Ivory's house. Sabrina and Ivory left their homes at the same time and arrived at the park at the same time. Sabrina drove at a speed of 76 km/h while Ivory drove at a speed 19 km/h slower than Sabrina. Leaving your answer in kilometres,

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

(a)
Let the distance between Sabrina's house and Ivory's house be 1 d.
Ivory travelled = ¹₂ d - 2000 m
Sabrina travelled = ¹₂ d + 2000 m

Distance that Sabrina travelled more than Ivory
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Sabrina took to travel to the park
= 4 ÷ 19
= ⁴₁₉ h

Distance that Sabrina travelled
= ⁴₁₉ x 76
= 16 km

1000 m = 1 km
2000 m = 2 km

Distance between Ivory's house and the museum
= 16 - 2
= 14 km

Answer(s): (a) 4 km; (b) 14 km