Jorge and Rosa drive towards Lake Murray. Jorge drives faster. How fast and long did each person drive?

Question

Jorge was 2 times faster than Rosa when driving toward Lake Murray. In fact, Jorge drove the 162 miles to Lake Murray in 2 hours less than it took Rosa to drive 135 miles. How fast and long did each person drive?

Answer 1

The equations are:

(135/V) = t (Rosa 135 miles)

(162/(2V))= t-2

(162/(2V))=(135/V)-2

solving for V

4V²-108V=0

V1=)

V real Rosa= 27 mph

V Jorge = 54 mph

Proof:

135/27 = 5

162/54 = 3

Check!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 

 

Answer 2

 

Jennifer:

 

Let Jorge's speed be j mph and Rosa's be r mph.

 

Jorge takes 162/j hours to drive 162 miles. Rosa takes 135/r hours to drive 135 miles.

 

We are given that Jorge takes two hours less. So if we add 2 to Jorge's hours we get Rosa's.

 

162/j + 2 = 135 / r.  We get (162 + 2 j ) / j = 135 / r 

 

But we are also given that Jorge drives two times faster than Rosa.  So, j = 2r.

 

Substituting in the above expression we get (162 + 4r) / 2r = 135 / r.  Cancel the r from the denominator on both sides. On the left, divide by 2.  Then 81 + 2r = 135.  Therefore 2r = 54, that is, r = 27 and, of course, j = 2 x 27 = 54.

 

Back check, please.  I have.  It is corrrrrrrect!

 

Dattaprabhakar (Dr, G,)

 

 

This is 2 hours less than Rosa takes (to drive 135 miles).

 

So Rosa takes (162/j) + 2 hours to drive 135 miles.

 

Rosa's spee

 

 

 

 

 

 

 

 

 

 

 

We are given that Jorge was two times faster than Rosa.  So Jorge's speed  must be 2R. (we need not use J any more)

 

Jorge takes 162 / (2R) hours to drive 162 miles. 162/(2R) = 81 / R.

 

This is two hours less that it takes Rosa. 

 

So Rosa takes (81 / R) + 2  = (81+2R)/ R hours to drive 135 miles.

 

Rosa's speed is 135 / [(81 + 2R) / R] = (135 R) / (81 + 2R)

Answer 3

      I just read the answers given to you for yesterdays problem. Although those are correct, I suspect that your teacher did it very differently. I figure you must be studying rational equations. I make students write out a table.

 

                  rate                time              distance

Jorge          2x                162/2x            162

Rosa            x                 135/x               135

 

Jorge's drive time is 2 hours less than Rosa's.

162/2x  = 135/x - 2           make common denominators

162/2x  = 270/2x - 4x/2x         multiply both sides by 2x

162  = 270 - 4x

-108 = -4x

27 = x

Always check to see if this number makes sense and if you answered the question.

Jorge traveled at 54mph for 162/54=3 hours for a total distance of 54*3=162.

Rosa traveled at 27mph for 135/27=5 hours for a total distance of 27*5=135.

Jorge IS twice as fast and DID travel 2 hours less....so we've got the right numbers.