What is the preferred approach for this problem?
Convert your training data to the following format - 

a = login_time
b = logout_time
c = person_activity
train_data_X = [
               [[a, b, c], [a, b, c], ......, [a, b, c]]
               [[a, b, c], [a, b, c], ......, [a, b, c]]
               .
               .
               .
               [[a, b, c], [a, b, c], ......, [a, b, c]]
             ]

train_data_Y = [
                 [[time_day_1], [time_day_2], ...... [time_day_60]]
                  .
                  .
                  .
                 [[time_day_1], [time_day_2], ...... [time_day_60]]
                ]


Explaination - 

You Input(training_data_X) data has shape 10000 * 60 * 3 because you have 10K users, data for 60 days and each data point depends on 3 variables namely a, b and c.
Your Target(training_data_Y) data has shape 10000 * 60 * 1 because you have just one number to output i.e active time.

Now, this is a Regression Problem because you are trying to predict a continuous value i.e active time.

You can model this type of problem with a number of time-series models. But since you got a multivariate input, i.e [a, b, c](refer training_data_X). You would be benefitted a lot using a Seq2Seq model to generate your time-series. If just want to generate 61st time-step you could use it just for that as well.

Specific details and implementation