A city's bus system has a red-line and a blue-line. Both a red-line bus and a blue-line bus are currently at the City Hall Station. If a red-line bus arrives at the City Hall Station every 12 minutes and a blue-line bus arrives at the City Hall Station every 10 minutes, after how many minutes will the two buses next arrive at the City Hall Station at the same time?

Step-by-step explanation:

Given that the arrival time of the redline bus= 12minutes

arrival rate = 1/12 arrival per minutes

arrival time of the blueline bus= 10minutes

arrival rate = 1/10 arrival per minutes

the combined arrival rate is given by the expression

let redline be A

and blueline be B

and let the combines arrival rate be x

A+B/(A*B)=1/x

1/12+1/0=1/x

12+10/12*10=1/x

22/120=1/x

x=120/22

x=5.45minutes

29.5977692753

step-by-step explanation:

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step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse