problem below

Question

Working together, a man and his two sons assembled a set of electric trains in 12 minutes. working alone, it would have taken the man 10 minutes less than it would have taken either son working alone. how long would it have taken the two sons, working together without their father, to assemble the set of trains?

 

Need help quick

Answer 1

The father can complete 1 train set in x minute   R_F = 1/x

Either son can complete one rain set in x + 10 minutes  R_S =  1/(x+10)

Together they can complete one train set in 12 minutes  R_T = 1/12

 

1/x + 1/(x +10) + 1/(x+10) = 1/12

(3x + 10)/(x² + 10x) = 1/12

36x + 120 = x² + 10x

0 = x² -26x -120 

 

which can be factored

 

0 = (x - 30)(x + 4)

 

-4 minutes is not a possible solution, so the father, working alone, takes 30 minutes

 

Either son, working alone, take 30 +10 = 40 minutes

 

Working together, the boys have a rate of R_B = R_S+ R_S = 1/40 + 1/40 = 1/20,  

so, together, the boys accomplish the job in 20 minutes.