A park and a museum, 500 m apart, are situated between Shiyun's house and Xylia's house. The museum is halfway between the two houses and the park is closer to Xylia's house. Shiyun and Xylia left their homes at the same time and arrived at the park at the same time. Shiyun drove at a speed of 70 km/h while Xylia drove at a speed 10 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

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

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

Distance that Shiyun travelled
= ¹₁₀ x 70
= 7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Xylia's house and the museum
= 7 - 0.5
= 6.5 km

Answer(s): (a) 1 km; (b) 6.5 km