A park and a museum, 1500 m apart, are situated between Irene's house and Gem's house. The museum is halfway between the two houses and the park is closer to Gem's house. Irene and Gem left their homes at the same time and arrived at the park at the same time. Irene drove at a speed of 76 km/h while Gem drove at a speed 16 km/h slower than Irene. Leaving your answer in kilometres,

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

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

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

(b)
Time that Irene took to travel to the park
= 3 ÷ 16
= ³₁₆ h

Distance that Irene travelled
= ³₁₆ x 76
= 14.25 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Gem's house and the museum
= 14.25 - 1.5
= 12.75 km

Answer(s): (a) 3 km; (b) 12.75 km