Confused :(

Question

A train moving at r miles per hour can cove a given distance in h hours. By how many miles per hour must its speed be increased in order to cover the same dist in one hour less time

Answer 1

OK:

 

Scenario corresponds to this equation:

 

(r+x)(h-1)=hr

x - is the increment in original speed which makes travel 2 times faster.

 

solve for x; you'll find x=r/(h-1)

 

{CHECK:

 

(r+x)(h-1)=r+hr-r=hr }

Answer 2

 A train is moving at r mi/hr can cover a given distance in h hours. By how many mi/he must its speed be increased in order to cover the same distance in one hours less time?

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  With such problems, one of the variables is the same or related so we can solve the problem. In this problem, we are told that it is "the same distance.”

 

So, let's set the distances equal:

          train's distance at initial speed                train's distance at increased speed and less time

    D =           (r mi/hr)*(h hr)                =             ( (r+x) mi/hr )*((h-1) hr)

             Notice how hours cancel out, leaving only miles.

                rh = (r+x)(h-1)  miles

        But we want to know increase in rate (miles/hr) x.

               rh = rh - r + xh - x                            (using FOIL)

               0 = -r + xh -x                                  (subtract rh from both sides)

               0 = x(h-1) -r                                  (distributive property)

               x(h-1) = r                               (just rearranging)

              x = r/(h-1)  miles/hr

 

Now, be very careful of the words, "By how many mi/he must its speed be increased" because the problem is not asking for the new speed; it is not asking for the percent increase in speed; it is asking for the net unit increase in speed (for example, from 40 to 60 mph is an increase of 20 mph; don't  say 60 or 50%).

 

Let's test those example numbers, "A train moving at 40 mi/hr can cover a given distance in 3 hours. By how many mi/he must its speed be increased in order to cover the same distance in one hours less time?"  To cover 120 miles (40*3) in 2 hours (1 hour less time), the train must increase its speed by 20 mph to 60 mph -- the answer for this example is 20 mph).  We calculate that as (r)/(h-1) = (40)/(2) = 20 mph.

 

Answer 3

 

Lisa,

 

If a train is moving at the speed of r mi/hr for h hours,

the distance traveled, D, is r·h.

 

If x denotes the speed

with which the train can travel the same distance, D, in (h-1) hours,

we get

 

     D = r·h

     

         = x·(h-1)

 

Solving the above equation, we get x = r·h/(h-1).

 

So, we need to increase the speed by r/(h-1) to r·h/(h-1).

 

 

 

Answer 4

I'd like to help you answer this but I am confused by your problem. Can you type it all out again, it seems to be missing some words.