A salon and a cafe, 500 m apart, are situated between Min's house and Usha's house. The cafe is halfway between the two houses and the salon is closer to Usha's house. Min and Usha left their homes at the same time and arrived at the salon at the same time. Min drove at a speed of 76 km/h while Usha drove at a speed 16 km/h slower than Min. Leaving your answer in kilometres,

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

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

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

(b)
Time that Min took to travel to the salon
= 1 ÷ 16
= ¹₁₆ h

Distance that Min travelled
= ¹₁₆ x 76
= 4.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Usha's house and the cafe
= 4.75 - 0.5
= 4.25 km

Answer(s): (a) 1 km; (b) 4.25 km