A park and a museum, 3500 m apart, are situated between Jane's house and Mary's house. The museum is halfway between the two houses and the park is closer to Mary's house. Jane and Mary left their homes at the same time and arrived at the park at the same time. Jane drove at a speed of 61 km/h while Mary drove at a speed 20 km/h slower than Jane. Leaving your answer in kilometres,

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

(a)
Let the distance between Jane's house and Mary's house be 1 d.
Mary travelled = ¹₂ d - 3500 m
Jane travelled = ¹₂ d + 3500 m

Distance that Jane travelled more than Mary
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Jane took to travel to the park
= 7 ÷ 20
= ⁷₂₀ h

Distance that Jane travelled
= ⁷₂₀ x 61
= 21.35 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Mary's house and the museum
= 21.35 - 3.5
= 17.85 km

Answer(s): (a) 7 km; (b) 17.85 km