A contractor rented a sander for 5h and a polisher for $50. For another job, she rented the sander for 4h and the polisher for 8h. The rental fees for the job totalled $56. Find the hourly rate charged for each tool.
Sander = X Dollars / hr.
Polisher = Y Dollars/hr
Eq1: 5X + 5Y = 60.
Eq2: 4X + 8Y = 56.
Multiply Eq1 by -4 and Eq2 by 5 and add.
-20X - 20Y = -200.
20X + 40Y = 280.
20Y = 80,
Y = 80 / 20 = 4.
Substitute 4 for Y in Eq1:
5X + 5*4 = 50,
5X + 20 = 50,
5X = 50 - 20 = 30,
X = 30 / 5 = 6.
To find the hourly rate charged for each tool, let's assume the hourly rate for the sander is "s" and the hourly rate for the polisher is "p".
Given information:
- The contractor rented the sander for 5 hours and the polisher for $50. So, we can write the equation: 5s + 50 = total rental fee for the first job.
- The contractor rented the sander for 4 hours and the polisher for 8 hours. The rental fees for this job totaled $56. So, we can write the equation: 4s + 8p = 56.
Now, we can use these equations to solve for "s" and "p".
From the first equation, 5s + 50 = total rental fee for the first job, we can rearrange it to get:
5s = total rental fee for the first job - 50.
From the second equation, 4s + 8p = 56, we can rearrange it to get:
8p = 56 - 4s.
Now, substitute the value of 8p from the second equation into the first equation:
5s + 50 = 56 - 4s.
Combine like terms:
5s + 4s = 56 - 50,
9s = 6.
Divide both sides by 9:
s = 6/9,
s = 2/3.
So, the hourly rate charged for the sander is 2/3 or $0.67 per hour.
To find the hourly rate for the polisher, substitute the value of s into either of the original equations. Let's use the second equation:
4(2/3) + 8p = 56.
Multiply both sides by 3 to eliminate the fraction:
8 + 24p = 168.
Rearrange the equation:
24p = 168 - 8,
24p = 160.
Divide both sides by 24:
p = 160/24,
p = 20/3.
So, the hourly rate charged for the polisher is 20/3 or $6.67 per hour.
Therefore, the hourly rate charged for the sander is $0.67 and the hourly rate charged for the polisher is $6.67.