A park and a museum, 500 m apart, are situated between Cathy's house and Julie's house. The museum is halfway between the two houses and the park is closer to Julie's house. Cathy and Julie left their homes at the same time and arrived at the park at the same time. Cathy drove at a speed of 78 km/h while Julie drove at a speed 13 km/h slower than Cathy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Cathy took to travel to the park
= 1 ÷ 13
= ¹₁₃ h

Distance that Cathy travelled
= ¹₁₃ x 78
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Julie's house and the museum
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km