A park and a museum, 500 m apart, are situated between Natalie's house and Vanessa's house. The museum is halfway between the two houses and the park is closer to Vanessa's house. Natalie and Vanessa left their homes at the same time and arrived at the park at the same time. Natalie drove at a speed of 61 km/h while Vanessa drove at a speed 10 km/h slower than Natalie. Leaving your answer in kilometres,

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

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

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

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

Distance that Natalie travelled
= ¹₁₀ x 61
= 6.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Vanessa's house and the museum
= 6.1 - 0.5
= 5.6 km

Answer(s): (a) 1 km; (b) 5.6 km