A park and a museum, 2500 m apart, are situated between Joelle's house and Raeann's house. The museum is halfway between the two houses and the park is closer to Raeann's house. Joelle and Raeann left their homes at the same time and arrived at the park at the same time. Joelle drove at a speed of 72 km/h while Raeann drove at a speed 16 km/h slower than Joelle. Leaving your answer in kilometres,

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

(a)
Let the distance between Joelle's house and Raeann's house be 1 d.
Raeann travelled = ¹₂ d - 2500 m
Joelle travelled = ¹₂ d + 2500 m

Distance that Joelle travelled more than Raeann
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Joelle took to travel to the park
= 5 ÷ 16
= ⁵₁₆ h

Distance that Joelle travelled
= ⁵₁₆ x 72
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Raeann's house and the museum
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km