A private plane takes 8 hours less to travel 960km than a car. If the plane travels 3 times as fast as the car, what is the speed of the plane and the car?

Question

Precalc 

Answer 1

Dear Carol,

    This is a rate*Time=distance (r*t=d) problem.  You might start by underlining or highlighting key words and

 

numbers in your story problem.

 

 

Question:  What is the speed of the plane and the car?

 

 

 

[____________________]  Car's distance =960 Km      

 

 

[____________________]  Plane's distance=960 Km        Both have traveled the same distance.

 

 

Then set up a little table to write down your data:                         t=time in hours of car

 

 

 

    Rate (Speed)    *      time (hours)     =       Distance

 

 plane   3X                             t-8          =      3X (t-8) =    960 Km

 

 car        X                               t            =         Xt      =      960 Km   

 

 

 

 

We want the speed of the plane, so we are looking for "X."   Also,  you now have a system of two equations.  You

 

need to have both equations with only the variable "X."  Here elimination can be used, along with substitution.

 

 

3X (t-8) =960

 

     Xt=960               Divide both sides by the "X" to get rid of it.

 

      t=960/X            Now substitute this value of "X" into the first equation.

 

3(X)( (960/X)  - 8)  =960         Use the distributive property.

 

3X (960/X)    -24X  =960       For the first term, the "X" in the numerator will cancel with the "X" in the

 

denominator.

 

 

 2880 -24 X   = 960       Add "24 X"  to both sides of the equation.

 

2880-24X + 24X = 960 +24X      Now subtract 960 from both sides of the equation, and simplify the equation.

 

2880-960 = 24X                         1,920= 24X      Next, divide both sides of equation by 24, and you

 

will have solved for "x= speed of car."   3X= speed of plane

 

     I am going to let you complete this problem.  You can go further with this problem by checking your answers.  It is easy to find out through substitution the time it took for the car and the plane to travel 960 Km.  Then if you have both the "X" and the "t" values, you can check to see if everything is true in the equation by substituting your answers into it.

 

If I have helped you, please give me a thumbs up.

 

                                                                  Susan C.