rate of first --- $x
rate of 2nd ---- $ (160-x)
5x + 15(160-x) = 1750
5x + 2400 - 15x = 1750
-10x = -650
x = 65
1st one charged $65 per hour
2nd charged $95 per hour
check:
5(65) + 15(95) = 1750
65+95 = 160
rate of 2nd ---- $ (160-x)
5x + 15(160-x) = 1750
5x + 2400 - 15x = 1750
-10x = -650
x = 65
1st one charged $65 per hour
2nd charged $95 per hour
check:
5(65) + 15(95) = 1750
65+95 = 160
We are given that the two mechanics worked together for a total of 5 + 15 = 20 hours. And the total amount charged for their work was $1750.
Now, let's set up two equations:
Equation 1: R1 + R2 = 160 (since the sum of their rates is 160 per hour)
Equation 2: R1 * 5 + R2 * 15 = 1750 (since the total amount charged is $1750)
We can solve these two equations simultaneously to find the values of R1 and R2.
Using Equation 1, we can find the value of R1:
R1 = 160 - R2
Substituting this value of R1 into Equation 2, we get:
(160 - R2) * 5 + R2 * 15 = 1750
800 - 5R2 + 15R2 = 1750
10R2 = 950
R2 = 95
Now we can substitute the value of R2 back into Equation 1 to find R1:
R1 = 160 - R2
R1 = 160 - 95
R1 = 65
Therefore, the rate charged per hour by the first mechanic is $65, and the rate charged per hour by the second mechanic is $95.