Performing a pushup for an inexperienced client or someone who is elderly can be a challenge. Some elderly men and women have a hard time getting on their knees. Even a simple half pushup from the knees in not possible if they have had knee surgery recently.
Using a barbell in a squat rack is a safe and effective way to have the client work the chest and triceps, without risk to the knees. Some personal trainers have their clients perform pushups against the wall, but I have found that this ads stress to the carpel bones and wrist ligaments, because of the unnatural dorsal flexing of the hand.
By using a bar in the rack, set at a height that is challenging, yet safe, seems to be a better alternative to the pushup for the elderly.
https://youtu.be/HUpAh-uqa0g