Researchers at Ball State University did a study on this exact topic.
They found that the time savings was about 30 percent. In other
words, you could achieve in about 7 weeks under a personal trainer
what it would take you 10 weeks to do on your own.
The Ball State researchers compared two groups of people. One group
worked out under the supervision of fitness trainers. The other group
worked out without trainers. The researchers found that the group
supervised by trainers achieved muscle strength in 30 percent less
"... there were no differences in the two groups at the start of the
study, but after 12 weeks it was obvious the supervised group had made
improvements over their unsupervised counterparts.
Individuals in the supervised group not only increased their muscle
size, but also reached that level in 30 percent less time.
The supervised group may also have benefitted from the personal
attention of the trainers, who provided motivation in reaching certain
"Direct supervision can help people get fit faster."
Ball State University
The same study (and 30 percent time-savings figure) was reported in
South Africa's Sunday Times:
"The Power Of 1-On-1
A personal trainer puts the punch in your workout, according to
researchers. In a report in the August issue of Medicine & Science in
Sports & Exercise, gym-goers who use a personal trainer may see better
results, sooner than those who curl, lift and squat alone. A group of
20 men were out through 12 weeks of strength training, in which they
were given the same exercises to do - stomach crunches, squats and
bench presses. While all the men improved their strength, those given
one-on-one instruction gained more power in about 30 percent less time
than did the control group. The researchers said a possible reason for
the one group gaining the edge is that the personal trainers gave
their clients a psychological boost. - - courtesy of Longevity
source: Sunday Times, South Africa
Here are two good articles if you're thinking about getting a fitness trainer:
Do You Need A PERSONAL TRAINER?
Ebony Magazine, hosted by Findarticles.com
Shopping for a personal trainer: following these six steps can mean
the difference between failure and a great-looking body
Men's Fitness, hosted by Findarticles.com
"personal trainer", "percent less time"
I hope this helps.