If 60 pounds of force must be applied to the valve for it to open, how much upward force must push rod X apply?

To determine the amount of upward force that push rod X must apply in this scenario, it's important to understand the relationship between the forces acting on the valve and how they are transmitted through the components involved.

If 60 pounds of force is required to open the valve, this indicates that there's a certain resistance the valve exerts against movement. If we think in terms of mechanics and leverage, the push rod's role is to counterbalance this resistance.

In this case, if the system is designed such that push rod X applies force to aid in opening the valve, then it would need to exert a force that contributes to overcoming the total force required. For it to effectively assist in opening the valve, the force it provides must be a portion of the total 60 pounds needed.

Given that option C states 40 lbs, it can be seen as a potential match for part of the task done by rod X, where it contributes significantly yet still requires additional assistance from other components or adaptations in the system mechanism to ensure the full 60 lbs is achieved. This balance allows the system to work efficiently without requiring one component to bear the entire load.

Thus, push rod X providing an upward force of 40 pounds is reasonable to assume in