Make this chart:


                                 distance  = rate × time
from home to bus stop jogging |           |      |      | 
from bus stop to work riding  |           |      |      |
totals riding & jogging       |           |      |      |

Let x be the answer. So we fill in x for the time from home to
the bus stop jogging

                                 distance  = rate × time
from home to bus stop jogging |           |      |  x   | 
from bus stop to work riding  |           |      |      |
totals riding & jogging       |           |      |      |

Next we fill in the rates of 6 mph and 30 mph

                                 distance  = rate × time
from home to bus stop jogging |           |   6  |  x   | 
from bus stop to work riding  |           |  30  |      |
totals riding & jogging       |           |      |      |

We fill in the total time of 1 hour

                                 distance  = rate × time
from home to bus stop jogging |           |   6  |  x   | 
from bus stop to work riding  |           |  30  |      |
totals riding & jogging       |           |      |  1   |

We fill in the total distance of 22 miles

                                 distance  = rate × time
from home to bus stop jogging |           |   6  |  x   | 
from bus stop to work riding  |           |  30  |      |
totals riding & jogging       |     22    |      |  1   |

Use Distance = Rate × Time to fill in her distance jogging to the
bus stop from home.

                                 distance  = rate × time
from home to bus stop jogging |     6x    |   6  |  x   | 
from bus stop to work riding  |           |  30  |      |
totals riding & jogging       |     22    |      |  1   |
 
Use the principle:     

      Time riding = Total time riding and jogging -  time jogging  

to fill in the time from the bus stop to work riding the bus as 1-x.    

                                 distance  = rate × time
from home to bus stop jogging |     6x    |   6  |  x   | 
from bus stop to work riding  |           |  30  | 1-x  |
totals riding & jogging       |     22    |      |  1   |

Fill in the distance riding the bus using

                                         distance = rate × time

                                 distance  = rate × time
from home to bus stop jogging |     6x    |   6  |  x   | 
from bus stop to work riding  |  30(1-x)  |  30  | 1-x  |
totals riding & jogging       |     22    |      |  1   |
                                            
Now we form the equations from the principle:

Distance jogging + Distance riding = Total distance jogging and riding:

                  6x + 30(1-x) = 22

Solve that and get x =  of an hour or  =
20 minutes jogging and 40 minutes riding.

So the answer asked for is 20 minutes jogging.

Edwin