A park and a museum, 1500 m apart, are situated between Jane's house and Pamela's house. The museum is halfway between the two houses and the park is closer to Pamela's house. Jane and Pamela left their homes at the same time and arrived at the park at the same time. Jane drove at a speed of 66 km/h while Pamela drove at a speed 20 km/h slower than Jane. Leaving your answer in kilometres,

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

(a)
Let the distance between Jane's house and Pamela's house be 1 d.
Pamela travelled = ¹₂ d - 1500 m
Jane travelled = ¹₂ d + 1500 m

Distance that Jane travelled more than Pamela
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Jane took to travel to the park
= 3 ÷ 20
= ³₂₀ h

Distance that Jane travelled
= ³₂₀ x 66
= 9.9 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Pamela's house and the museum
= 9.9 - 1.5
= 8.4 km

Answer(s): (a) 3 km; (b) 8.4 km