A park and a museum, 1500 m apart, are situated between Wendy's house and Erika's house. The museum is halfway between the two houses and the park is closer to Erika's house. Wendy and Erika left their homes at the same time and arrived at the park at the same time. Wendy drove at a speed of 70 km/h while Erika drove at a speed 20 km/h slower than Wendy. Leaving your answer in kilometres,

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

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

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

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

Distance that Wendy travelled
= ³₂₀ x 70
= 10.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Erika's house and the museum
= 10.5 - 1.5
= 9 km

Answer(s): (a) 3 km; (b) 9 km