How can you calculate distance when given power, time, and mass?
power used to lift crate is 3490, mass of crate is 425 kg, time is 3 seconds. how far was the crate lifted?

First step:         Power = (work done) / (time to do the work).

                 3490 watts = (work done) / (3 seconds)

     3490 joules/second = (work done) / (3 seconds)

Multiply each side by 3 seconds:

     Work done = (3490 x 3) joules  =  10,470 joules 

Second step:       Weight = (mass) x (gravity)

                 Weight of the crate = (425 kg) x (9.8 m/s²)

                                              =  4165 newtons

Step 3:     Work done  =  (force) x (distance)

                                 =  (weight) x (distance lifted)

            10,470 joules  =  (4165 newtons) x (distance)

Divide each side by 4165 newtons:

       Distance = 10,470 kg-m²/sec² / 4165 kg-m/s²

                     =        2.514... meters  (rounded)

You asked:  "How can you calculate ... ?"
Notice that I did the same thing in all 3 steps ... write down the formula
for finding a quantity, then write the numbers you know into the formula
to find the quantity. 

THAT's "how", and it all boils down to knowing the formulas and picking
the right one to work with.  The right one to pick is the one that talks about
all (or most) of the quantities that you know AND the quantity that you're
trying to find. 

For example, if you need to find how long it will take your turtle to walk
across the room, then you need a formula that talks about time, speed,
and distance.  You would not get much help from the formula that talks
about the pressure and volume of a gas, or one that talks about the
frequency and wavelength of light waves, or Einstein's formula  E=mc² 
for the equivalency of mass and energy.