A park and a museum, 2500 m apart, are situated between Xylia's house and Gabby's house. The museum is halfway between the two houses and the park is closer to Gabby's house. Xylia and Gabby left their homes at the same time and arrived at the park at the same time. Xylia drove at a speed of 72 km/h while Gabby drove at a speed 18 km/h slower than Xylia. Leaving your answer in kilometres,

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

(a)
Let the distance between Xylia's house and Gabby's house be 1 d.
Gabby travelled = ¹₂ d - 2500 m
Xylia travelled = ¹₂ d + 2500 m

Distance that Xylia travelled more than Gabby
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Xylia took to travel to the park
= 5 ÷ 18
= ⁵₁₈ h

Distance that Xylia travelled
= ⁵₁₈ x 72
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Gabby's house and the museum
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km