A park and a museum, 1500 m apart, are situated between Shiyun's house and Nora's house. The museum is halfway between the two houses and the park is closer to Nora's house. Shiyun and Nora left their homes at the same time and arrived at the park at the same time. Shiyun drove at a speed of 60 km/h while Nora drove at a speed 10 km/h slower than Shiyun. Leaving your answer in kilometres,

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

(a)
Let the distance between Shiyun's house and Nora's house be 1 d.
Nora travelled = ¹₂ d - 1500 m
Shiyun travelled = ¹₂ d + 1500 m

Distance that Shiyun travelled more than Nora
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Shiyun took to travel to the park
= 3 ÷ 10
= ³₁₀ h

Distance that Shiyun travelled
= ³₁₀ x 60
= 18 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Nora's house and the museum
= 18 - 1.5
= 16.5 km

Answer(s): (a) 3 km; (b) 16.5 km