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

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

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

Distance that Zoe travelled more than Yoko
= 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 68
= 12.75 km

1000 m = 1 km
1500 m = 1.5 km

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

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