Thanks for your feedback which is most useful. 
The reason that the timing is not given in the music, is this would significantly slow down the learning process as you would have to read the timing for every single note. 
If you are familiar with the tune, most people find it easy to Play the timing of the melody by reference to the words of the song. I don’t recommend students try playing songs that they are not familiar with as this makes life really hard and misses out on the motivation which is gained by playing a song that you like already. 

The timing of the cards is usually a constant number of beats e.g. four beats and again, the timing of the chords are played by following the words of the song.

In addition, if you play along with a demonstration of the song, this also shows you the rhythm. You can slowdown the videos e.g. to half speed to make this easier to play along to, when you are learning. 

I hope that this helps.

Thanks
Declan