word problem

Question

Totsakan left the airport and traveled toward the ferry office. Amanda left one hour later traveling at 36 mph in an effort to catch up to Totsakan. After traveling for five hours, Amanda finally caught up. Find Totsakan's average speed.

Answer 1

Sometimes it is easy just to find the answer, but the problem was written to help you learn a process or how to use a formula.

 

This is a D-I-R-T (Distance-Is-Rate-times-Time, or D=RT) problem.  With such problems, one of the variables is equal or has a relationship with another variable -- that's so we can solve the problem.  Here, the distance is the same (we really don't care what it is).

 

Here are:                D miles              R mph                  T hours

  for Totsakan          (same)            r (to find)             1 + 5 hours

  for Amanda           (same)             36 mph                  5 hours

 

Set the distances equal (since they are the same):

           D  =  r(1+5) = (36)(5)      [note:  with mph*hr, hr cancels our leaving only miles)

Solve for r as requested:

              6r = 180

               r = 30 mph

Answer 2

Since Amanda caught up after 5 hours, she had gone 5 times 36 or 180 miles.  (rate times time equals distance)

Totsakan had to go the same distance in six hours so he or she was going 180/6 = 30 mph. (distance / time equals rate)

Answer 3

Dear Marlene,

    Here is another way of thinking about the problem: 

 

1.  Draw a little sketch and then a table.

 

 

Tot.                   Airpot    ._____________________>Fairy Office      Distance one=  d₁

 

Amanda            Airport   ._____________________> Fairy Office      Distance two=d₂

 

When they catch up, their distances are the same.

 

 

2.  When Amanda caught up with Tot. at 5 hours, Totsakan had already been traveling one hour more, 6 hours.

 

 

3.  Let r= Totsakan's rate of speed               t=Amanda's time              t+1= Totsakan's time

 

 

 

4.  Now, make a table to match the data:    Rate * time= distance

 

               rate (speed mi/hour)        *              time (hours)       =             Distance

Totsakan      r                                               ( 5+1)                 =   6r___= d₁_____

 

Amanda       36 mi/h                                        5                     =     36*5=180=d₂

 

 

Here you can finish the problem.

 

 

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

 

                                               Susan C.

 

 

Answer 4

This is a distance-rate-time problem and d=rt

 

For Totsaken, d = r (6).  It's 6 hours because Amanda left an hour after Totsakan and traveled 5 hours before catching up.

For Amanda, d = 36 (5)

 

The d's are equal because Amanda catches up to Totsakan.

 

Since they are equal we can set the two equal to one another and solve for r, Totsakan's rate of travel (i.e. average speed)

 

6r = 36 (5)

r = 30

 

So Totsakan is traveling 30 mph.

 

Hope that helps.