Sam went to the park traveling 15 mph and returned home traveling 30 mph. If the total trip took 9 hours, how long did Sam travel at each speed?

Question

I am trying to find the number of hours at 15mph and the number of hours at 30mph

Answer 1

David W.'s way of working it out is the correct way for

most situations involving distance = rate * time problems.

However; looking at the information here we see that

he travelled 15mph going and 30mph returning.

That means it took 2 times as long to get there as it

did to return since the speed was exactly double.

 

g = 2r     where g=time going, r = time returning

g+r = 9   total time 9 hours

 

substituting 2r for g in 2nd equation

 

2r + r = 9

3r = 9

r = 3

It took 3 hours to return

9-3 = 6 hours going

Answer 2

With problems such as this, look for (1) something that is the same and (2) items that have an equation relating them.  These allow us to solve the problem.

 

In this problem, (1) the distance each way is equal and (2) the total time is 9 hours (one is t and the other is 9-t).

 

The formula is:     D = R * T             [remember D-I-R-T; Distance Is Rate*Time]

 

    Distance to               =              Distance From

   (15 mph)*t               =             (30 mph)*(9-t)             [let t = time travelling "to"]

 

The math:

     15t = 270 - 30t

     45t = 270

        t = 6 hours             [note: be sure that units match]

 

   It took 6 hours to get there and 3 hours to get back.

 

Not asked, but a good check:

    Distance to             =         Distance From

       15*6                   =          30*3

                    90          =      90           Check!