A park and a museum, 1000 m apart, are situated between Pamela's house and Min's house. The museum is halfway between the two houses and the park is closer to Min's house. Pamela and Min left their homes at the same time and arrived at the park at the same time. Pamela drove at a speed of 63 km/h while Min drove at a speed 15 km/h slower than Pamela. Leaving your answer in kilometres,

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

(a)
Let the distance between Pamela's house and Min's house be 1 d.
Min travelled = ¹₂ d - 1000 m
Pamela travelled = ¹₂ d + 1000 m

Distance that Pamela travelled more than Min
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Pamela took to travel to the park
= 2 ÷ 15
= ²₁₅ h

Distance that Pamela travelled
= ²₁₅ x 63
= 8.4 km

1000 m = 1 km
1000 m = 1 km

Distance between Min's house and the museum
= 8.4 - 1
= 7.4 km

Answer(s): (a) 2 km; (b) 7.4 km