How long would it take car number two to catch up to car number one

Question

 How long would it take car number two to catch up to car number one 

Answer 1

This is a classic D-I-R-T (Distance-Is-Rate-times-Time) problem.

 

With such problems, one variable is the same or related to another variable so that we may solve the problem.

 

Note:  It often helps to draw a picture.

 

In this problem, you have:

     Car Number One             with   D₁ = R₁ * T₁

     Car Number Two             with   D₂ = R₂ * T₂

 

Now, it should be obvious that Car Number One is travelling at a different rate (that is, speed) than Car Number Two.  How else, could it "catch up?"

 

Then, realize that "catch up" means to be at the same place at the same time.  So, determine whether they started at the same time and whether they have travelled the same distance (that is, also started from the same place).

    If they started at the same time:     T₁ = T₂

    If they started at the same place:     D₁ = D₂

Also, realize that either T or D must be different, because if they both started at the same time and at the same place, there would be no "catch up" to find.

 

Now, one further complication is associated with D-I-R-T problems.  Often, you must solve for another variable before you may solve for the variable that the problem asks you to find (in this case, Time).   Also, once you find the value of that variable, you may put it into either equation to find the value of the desired variable.

 

Example:

    If Car One started the Rally Race one hour ago travelling at an average of 50 miles per hour, how far would it go before Cart Two, starting now and averaging 60 miles per hour, "catchess up" ?

 

                Car One:    D = 50*(T+1)

                Car Two:    D = 60*T

        Note that D is the same and the times differ by 1 hour.

 

                            50(T+1) = 60T

                            50T + 50  = 60T

                              -10T = -50

                                  T = 5 hours              (note: must solve for T before solving for D)

 

                 D = 50*(5+1) = 60*(5)

                  D = 300 miles