A park and a museum, 1500 m apart, are situated between Zoe's house and Betty's house. The museum is halfway between the two houses and the park is closer to Betty's house. Zoe and Betty left their homes at the same time and arrived at the park at the same time. Zoe drove at a speed of 64 km/h while Betty drove at a speed 16 km/h slower than Zoe. Leaving your answer in kilometres,

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

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

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

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

Distance that Zoe travelled
= ³₁₆ x 64
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Betty's house and the museum
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km