A park and a museum, 1500 m apart, are situated between Shiyun's house and Jean's house. The museum is halfway between the two houses and the park is closer to Jean's house. Shiyun and Jean left their homes at the same time and arrived at the park at the same time. Shiyun drove at a speed of 68 km/h while Jean drove at a speed 17 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

Distance that Shiyun travelled more than Jean
= 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 ÷ 17
= ³₁₇ h

Distance that Shiyun travelled
= ³₁₇ x 68
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jean's house and the museum
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km