translate the given information into a system of equations. the question is below

Question

three skilled laborers,peter,simon,and ian together can do a certain job on 20 hrs. peter and simon can do it in 30 hrs simon and ian can do it in 40 hrs.how long would it take to do the job alone ?

Answer 1

 

 Recall that if they job can be done in T hours, then the workrate is 1/T jobs per hour.

 

 Their respective speeds are 1/P , 1/S, 1/I

 

 Their combined workrate speed is 1/20, so 1/P + 1/S + 1/I = 1/20; this is the 1st equation

 

1/P+ 1/S = 1/30 <--- Peter and simon finish the job is 30 hours; this is the 2nd equation

 

1/S + 1/I = 1/40 <--- Simon and Ian can complete the job is 40 hours; this is the 3rd equation

 

 

Equation #1 MINUS Equation 2:

 

1/I = 1/20 - 1/30 = (30 - 20)/600 = 10/600 = 1/60

I=60

Ian can complete the job in 60 hours working alone.

 

 

Equation 1 MINUS Equation 3:

1/P = 1/20 - 1/40 = (40-20)/800 = 20/800 = 1/40

P = 40

Peter can do the job in 40 hours working alone.

 

 

1/40 + 1/S + 1/60 = 1/20

 

3 + 120/s + 2 = 6 <--- multiplies everything by 120

 

120/s = 1

 

s = 120

 

Simon can complete the job in 120 hours working alone.