My ancient Schwinn is still a great bike for training, and it's 30 years old.

The pedals on my new road bike absolutely will not work on it! Neither will most of the other parts! They simply are not compatable--the screws are different sizes! Older 10 speeds also use 17 1/4 wheels, not 700c. Hard to get tires, tubes, and spokes for wheels--not to mention replacement wheels.

The last bike shop that did cable work for me had to go to the hardware store and jury rig various components together.

So whether or not your MTB pedals will work depends on how old that Murray is. There may also be other compatability problems.