A park and a museum, 500 m apart, are situated between Yoko's house and Natalie's house. The museum is halfway between the two houses and the park is closer to Natalie's house. Yoko and Natalie left their homes at the same time and arrived at the park at the same time. Yoko drove at a speed of 78 km/h while Natalie drove at a speed 10 km/h slower than Yoko. Leaving your answer in kilometres,

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

(a)
Let the distance between Yoko's house and Natalie's house be 1 d.
Natalie travelled = ¹₂ d - 500 m
Yoko travelled = ¹₂ d + 500 m

Distance that Yoko travelled more than Natalie
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Yoko took to travel to the park
= 1 ÷ 10
= ¹₁₀ h

Distance that Yoko travelled
= ¹₁₀ x 78
= 7.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Natalie's house and the museum
= 7.8 - 0.5
= 7.3 km

Answer(s): (a) 1 km; (b) 7.3 km