A park and a museum, 1500 m apart, are situated between Jaslyn's house and Jean's house. The museum is halfway between the two houses and the park is closer to Jean's house. Jaslyn and Jean left their homes at the same time and arrived at the park at the same time. Jaslyn drove at a speed of 64 km/h while Jean drove at a speed 20 km/h slower than Jaslyn. Leaving your answer in kilometres,

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

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

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

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

Distance that Jaslyn travelled
= ³₂₀ x 64
= 9.6 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jean's house and the museum
= 9.6 - 1.5
= 8.1 km

Answer(s): (a) 3 km; (b) 8.1 km