A park and a museum, 500 m apart, are situated between Shiyun's house and Fanny's house. The museum is halfway between the two houses and the park is closer to Fanny's house. Shiyun and Fanny left their homes at the same time and arrived at the park at the same time. Shiyun drove at a speed of 80 km/h while Fanny drove at a speed 16 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

Distance that Shiyun travelled more than Fanny
= 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 ÷ 16
= ¹₁₆ h

Distance that Shiyun travelled
= ¹₁₆ x 80
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Fanny's house and the museum
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km