A salon and a cafe, 500 m apart, are situated between Shiyun's house and Min's house. The cafe is halfway between the two houses and the salon is closer to Min's house. Shiyun and Min left their homes at the same time and arrived at the salon at the same time. Shiyun drove at a speed of 63 km/h while Min drove at a speed 20 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

Distance that Shiyun travelled more than Min
= 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 salon
= 1 ÷ 20
= ¹₂₀ h

Distance that Shiyun travelled
= ¹₂₀ x 63
= 3.15 km

1000 m = 1 km
500 m = 0.5 km

Distance between Min's house and the cafe
= 3.15 - 0.5
= 2.65 km

Answer(s): (a) 1 km; (b) 2.65 km