A park and a museum, 500 m apart, are situated between Jaslyn's house and Xylia's house. The museum is halfway between the two houses and the park is closer to Xylia's house. Jaslyn and Xylia left their homes at the same time and arrived at the park at the same time. Jaslyn drove at a speed of 63 km/h while Xylia drove at a speed 10 km/h slower than Jaslyn. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jaslyn took to travel to the park
= 1 ÷ 10
= ¹₁₀ h

Distance that Jaslyn travelled
= ¹₁₀ x 63
= 6.3 km

1000 m = 1 km
500 m = 0.5 km

Distance between Xylia's house and the museum
= 6.3 - 0.5
= 5.8 km

Answer(s): (a) 1 km; (b) 5.8 km