A park and a museum, 500 m apart, are situated between Pamela's house and Julie's house. The museum is halfway between the two houses and the park is closer to Julie's house. Pamela and Julie left their homes at the same time and arrived at the park at the same time. Pamela drove at a speed of 67 km/h while Julie drove at a speed 20 km/h slower than Pamela. Leaving your answer in kilometres,

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

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

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

(b)
Time that Pamela took to travel to the park
= 1 ÷ 20
= ¹₂₀ h

Distance that Pamela travelled
= ¹₂₀ x 67
= 3.35 km

1000 m = 1 km
500 m = 0.5 km

Distance between Julie's house and the museum
= 3.35 - 0.5
= 2.85 km

Answer(s): (a) 1 km; (b) 2.85 km