A park and a museum, 1500 m apart, are situated between Zara's house and Sabrina's house. The museum is halfway between the two houses and the park is closer to Sabrina's house. Zara and Sabrina left their homes at the same time and arrived at the park at the same time. Zara drove at a speed of 68 km/h while Sabrina drove at a speed 16 km/h slower than Zara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Zara took to travel to the park
= 3 ÷ 16
= ³₁₆ h

Distance that Zara travelled
= ³₁₆ x 68
= 12.75 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Sabrina's house and the museum
= 12.75 - 1.5
= 11.25 km

Answer(s): (a) 3 km; (b) 11.25 km