# Solving Real World Math Problems Using Rate, Time, and Distance

Ok, first of all real world math problems require a discipline of organization. Let’s take a look at this example:

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An airplane takes off from an airport at 7:00am traveling at a rate of 350 miles/hour. Two hours later, a jet takes off from the same airport following the same flight path at 490 miles/hour. In how many hours will the jet catch up with the airplane?

First define what varies; in this case it is the time.

Define:

T = the time the airplane travels and T-2 = the time the jet travels (2 hours later than the airplane)

Create a Table:

Rate X Time = Distance
Airplane v t 350t
Jet 490 t - 2 490(t - 2)

It is stated in the real world math problem example that the airplane and the jet are coming from the same airport and following the same flight path.
At some point and time, the jet will catch up with the airplane, since it is going at a faster speed.
Therefore, we can set the distance of the airplane and the distance of the jet equal to one another to find out the “catch-up” time where they each will be traveling together.

Set Up and Solve:

350t = 490(t - 2)
350t = 490t - 980
350t - 350t = 490t - 980 - 350t
0 = 140t - 980
0 + 980 = 140t - 980 + 980
980 = 140t
980/140 = 140t/140
7 = t

t = 7 hours is the time the airplane is traveling. It will take (t-2) hours or (7-2) = 5 hours for the jet to catch up with the airplane.

Check List:

Hmmm … reflecting on this real world math problem using rate, time, and distance, I was just wondering if you have asked yourself the following questions.

• What rate are you studying for your exams?

• Have you spent time trying to practice problems that you are having or have had difficulty solving in the past?

• Have you traveled the full distance to learn and understand the math concepts taught so far from your Algebra teachers?

• Did you “catch-up” with all of your work?

• Have you filled in the area of work that has kept you puzzled by seeking help and not going around in circles?

• What proportion of time have you dedicated for you to work on Math problems?

• Have you distributed your time appropriately for each of your other subjects?

Careful planning and preparation is the key to solving real world math problems and being successful in math.

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