A park and a museum, 500 m apart, are situated between Gem's house and Lynn's house. The museum is halfway between the two houses and the park is closer to Lynn's house. Gem and Lynn left their homes at the same time and arrived at the park at the same time. Gem drove at a speed of 80 km/h while Lynn drove at a speed 16 km/h slower than Gem. Leaving your answer in kilometres,

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

(a)
Let the distance between Gem's house and Lynn's house be 1 d.
Lynn travelled = ¹₂ d - 500 m
Gem travelled = ¹₂ d + 500 m

Distance that Gem travelled more than Lynn
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Gem took to travel to the park
= 1 ÷ 16
= ¹₁₆ h

Distance that Gem travelled
= ¹₁₆ x 80
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Lynn's house and the museum
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km