A park and a museum, 2000 m apart, are situated between Esther's house and Nicole's house. The museum is halfway between the two houses and the park is closer to Nicole's house. Esther and Nicole left their homes at the same time and arrived at the park at the same time. Esther drove at a speed of 72 km/h while Nicole drove at a speed 15 km/h slower than Esther. Leaving your answer in kilometres,

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

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

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

(b)
Time that Esther took to travel to the park
= 4 ÷ 15
= ⁴₁₅ h

Distance that Esther travelled
= ⁴₁₅ x 72
= 19.2 km

1000 m = 1 km
2000 m = 2 km

Distance between Nicole's house and the museum
= 19.2 - 2
= 17.2 km

Answer(s): (a) 4 km; (b) 17.2 km