A park and a museum, 500 m apart, are situated between Emma's house and Gabby's house. The museum is halfway between the two houses and the park is closer to Gabby's house. Emma and Gabby left their homes at the same time and arrived at the park at the same time. Emma drove at a speed of 66 km/h while Gabby drove at a speed 15 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the park
= 1 ÷ 15
= ¹₁₅ h

Distance that Emma travelled
= ¹₁₅ x 66
= 4.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Gabby's house and the museum
= 4.4 - 0.5
= 3.9 km

Answer(s): (a) 1 km; (b) 3.9 km