In an assembly line of a factory, which produces networking switching hubs, two robots are utilized. The first one (A) is able to produce 40 microchips per hour, whereas the second one (B) produces 30 microchips per hour. For a total production of 400 microchips, the two robots operated for 12 hours. How many hours did each robot work?
(1) clearly define your variables: state what they represent and what their relations are in terms of the information given in the problem statement,
(2) setup your equations,
(3) solve the system,
(4) check/validate your solutions and
(5) summarize your findings in a sentence that refers to what the problem asked.
1) Let's define the variables:
- Let's represent the number of hours the first robot (A) worked as x.
- The number of hours the second robot (B) worked would be (12 - x), since the total hours worked is 12.
2) Setting up the equations:
- The first robot produces 40 microchips per hour, so the number of microchips produced by the first robot (A) would be 40x.
- The second robot produces 30 microchips per hour, so the number of microchips produced by the second robot (B) would be 30(12 - x).
- The total number of microchips produced is given as 400.
3) Solving the system:
To solve the system, we need to set up an equation using the given information.
40x + 30(12 - x) = 400
40x + 360 - 30x = 400
10x = 40
x = 4
So, the first robot (A) worked for 4 hours, and the second robot (B) worked for (12 - 4) = 8 hours.
4) Checking/validating the solution:
To validate the solution, we can substitute the values found into the equations:
- First robot (A): 40 * 4 = 160 microchips produced
- Second robot (B): 30 * 8 = 240 microchips produced
The sum of the microchips produced by both robots is indeed 400.
5) Summary of findings:
The first robot (A) worked for 4 hours, and the second robot (B) worked for 8 hours in order to produce a total of 400 microchips.