Expert: Abe Mantell - 1/2/2009

Question
Hello

This is an example of the type of problem I'm having trouble with. I'm looking for more than just the answer though. I need to understand the theory behind the problem so that I can solve other problems of this type and similar types...
A man drove from home at an average speed of 30mph to an airport. He then boarded a helicopter and flew to the corporate office at an average speed of 60mph. The entire distance was 150 miles. The entire trip took 3 hours. Find the distance from the airport to the corporate office.

I need to get the answer using 1 equation and 1 variable.

What I've figured out so far is...

 Distance from home to airport = 150 - D
Distance from airport to office = D
       Distance total distance = 150 miles [given]
    Speed from home to airport = 30 mph [given]
  Speed from airport to office = 60mph [give]
average speed from home-office = 50 [150 divided by 3]
    Time from house to airport = (150 - D) divided by 30
   Time from airport to office = D divided by 60
        Time total travel time = 3 hours [given]

Unfortunately I have no idea how to set up the actual equation. I have tried several different forms and always end up with the same answer: D = D. Which is accurate, but not a lot of help :). PLEASE HELP!!!

One last quick note: I am 37 years old and NOT in school. I am self teaching. In the past I've had experts hold back information in the spirit of not wanting to "help me cheat." I have been stuck on this problem for more than a month now due to the fact that none of the books I'm using have a worked out solution to this type of problem. It is not possible for you to help me cheat. You can only save my sanity by helping to end my frustration.:) Please give me as much detail as possible regarding this type of problem and how to properly set up a solution.

Thanks so much

Ernie


Answer
Hello Earnie,

Sorry to hear this problem, or ons like it, have been causing you so
much grief!  I hope I can help!

Looks like you are on the right path.
The key here is that distance=(rate)x(time) or D=RxT
Rearrange to get T=D/R (i.e. time = distance/rate)
The time to travel from home to the airport is: (150-D)/30 hrs
The time to travel from the airport to office is: D/60 hrs
Hence, the total time is the sum of those two, which we are
told is 3 hrs.  Thus, the equation you seek is:
(150-D)/30 + D/60 = 3

Multiplying by 60 on both sides (to simplify) yields:
2(150-D) + D = 180
300-2D+D=180
300-D=180
D=120

D=120 miles.

OK?  Was this helpful enough for you to feel confident in solving
other distance-rate-time problems???

TTYL, Abe