I would do a few things:
1. Shorten (or even eliminate) your initial cardio and devote that time to weight training. Increased workout density will increase the heart rate and get the lungs working anyway. Better to spend your time hitting the weights.
2. Explain to your friend your workout methodology. Perhaps if you institute a strict "I go, you go" set scheme, you will get in your typical exercises/sets and eliminate wasted time.
James 1:16-17 ESV
Do not be deceived, my beloved brothers. Every good gift and every perfect gift is from above, coming down from the Father of lights
With God's help...Mens sana in corpore sano