Can you find the number of hours the plumber worked on the house?

An electrician, a carpenter, and a plumber are hired to work on a house.

The electrician charges $20 per hour, the carpenter $25 and the plumber $30.

On the first day the 3 worked a total of 19.5 hours and earned a total of 472.50.

If the electrician worked 1.5 more hours than the carpenter did,

how many hours did the plumber work?

E + C + P = 19.5 hours

E = C + 1.5

Substitute

C + 1.5 + C + P = 19.5 hours

2C + P = 19.5 - 1.5 hours

P = 18 - 2C

20E + 25C + 30P = 472.50

20(C + 1.5) +25C+ 30(18 - 2C) = 472.50

20C + 30 + 25C + 540 - 60C = 472.50

60C - 45C = 570 - 472.50

15C = 97.5

C= 6.5

P = 18 - 2C

P = 18 - 13 = 5 HOURS

E = C + 1.5 = 8 HOURS

The plumber worked on the house for 5 hours.

850

e+c+p =19.5 hours

e= 1.5 c

substitute

1.5c+c+p =19.5 hours

2.5c+p =19.5 hours

P = 19.5 -2.5c

20e+25c+30p = 472.50

20(1.5C) +25C+ 30(19.5-2.5C) =472.50

30C+25C+ 585 -75C =472.50

55C-75C+585 =472.50

-20C = -112.50

C= 5.625

P =19.5 -2.5(5.625)

P =19.5 - 14.063 = 5.437 HOURS

E =1.5 (5.625) =8.438

he worked for 21 hrs