word problem doubt

Question

A train running with 7/11 of its own speed reached a place in 22 hours how much time could be saved if the train would have run at its own speed

now let train speed be x

                       D          =       S          *     T

new speed  7x/11/22     =      x*7/11   *    22

own speed  7x/11/22     =        x

 

now distance is same    d= 7x/11/22

 

equation should be

7x/11/22=x*7/11*22

 but answer get wrong

 

please explain me where i did wrong please explain me

Answer 1

Ok, you committed the mistake by being redundant:

 

First, you already know that the distance that will be covered is the same so just say D_7/11 = D_original

 

So you also know that D = S*T

 

D_7/11 = D_original

 

S_7/11*T_7/11 = S_original*T_original <-- this will be our working equation so let's examine the given:

 

S_7/11 is of course the 7/11 of S_original so:    S_7/11 = (7/11)*S_original

 

At 7/11 speed, the time used is 22 hrs so that's T_7/11 = 22

 

And the question is how much time can be saved, meaning, this would be the difference in time consumed.

 

Going back to the working equation, substituting the values:

 

(7/11)*S_orig*22 = S_orig*T_orig -------> The S_orig will be cancelled.

 

(7/11)*22 = T_orig

 

T_orig = 14 hrs.  (This is not the answer.)

 

Since the question is how much time is saved, you will compare 22hrs and 14hrs.

 

22 - 14 = 6 hrs. Meaning you will save 6 hrs if you use the original speed.