A park and a museum, 1500 m apart, are situated between Betty's house and Pamela's house. The museum is halfway between the two houses and the park is closer to Pamela's house. Betty and Pamela left their homes at the same time and arrived at the park at the same time. Betty drove at a speed of 62 km/h while Pamela drove at a speed 20 km/h slower than Betty. Leaving your answer in kilometres,

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

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

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

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

Distance that Betty travelled
= ³₂₀ x 62
= 9.3 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Pamela's house and the museum
= 9.3 - 1.5
= 7.8 km

Answer(s): (a) 3 km; (b) 7.8 km