A park and a museum, 500 m apart, are situated between Ivory's house and Vanessa's house. The museum is halfway between the two houses and the park is closer to Vanessa's house. Ivory and Vanessa left their homes at the same time and arrived at the park at the same time. Ivory drove at a speed of 78 km/h while Vanessa drove at a speed 15 km/h slower than Ivory. Leaving your answer in kilometres,

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

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

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

(b)
Time that Ivory took to travel to the park
= 1 ÷ 15
= ¹₁₅ h

Distance that Ivory travelled
= ¹₁₅ x 78
= 5.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Vanessa's house and the museum
= 5.2 - 0.5
= 4.7 km

Answer(s): (a) 1 km; (b) 4.7 km