A park and a museum, 1000 m apart, are situated between Wendy's house and Raeann's house. The museum is halfway between the two houses and the park is closer to Raeann's house. Wendy and Raeann left their homes at the same time and arrived at the park at the same time. Wendy drove at a speed of 65 km/h while Raeann drove at a speed 13 km/h slower than Wendy. Leaving your answer in kilometres,

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

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

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

(b)
Time that Wendy took to travel to the park
= 2 ÷ 13
= ²₁₃ h

Distance that Wendy travelled
= ²₁₃ x 65
= 10 km

1000 m = 1 km
1000 m = 1 km

Distance between Raeann's house and the museum
= 10 - 1
= 9 km

Answer(s): (a) 2 km; (b) 9 km