A park and a museum, 500 m apart, are situated between Mary's house and Olivia's house. The museum is halfway between the two houses and the park is closer to Olivia's house. Mary and Olivia left their homes at the same time and arrived at the park at the same time. Mary drove at a speed of 68 km/h while Olivia drove at a speed 16 km/h slower than Mary. Leaving your answer in kilometres,

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

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

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

(b)
Time that Mary took to travel to the park
= 1 ÷ 16
= ¹₁₆ h

Distance that Mary travelled
= ¹₁₆ x 68
= 4.25 km

1000 m = 1 km
500 m = 0.5 km

Distance between Olivia's house and the museum
= 4.25 - 0.5
= 3.75 km

Answer(s): (a) 1 km; (b) 3.75 km