Mathematics on Time and Distance

Problem given 

One car has a speed  of  204.2  Km/hr and other car has the speed  200 km/hr. Both the car started simultaneously , but the second car reached the same distance after  7 seconds of the first car. What is the distance and what will be time required for both the cars .


Solution:

Let , the distance be X   km and let the time taken for the  first car be T hr. to cover the entire distance.
Time taken for the first car T =  X/ 204.2 Hr.
Naturally other car has taken T Hr + 7 secs to cover that distance

Now , for the first car , at the speed of  204.2 km/hr at T hr it will traverse 204.2 T Km.

and for the second car at the speed of 200 Km/hr. at (T+ 7/3600) Hrs. it will cover the same distance of  200 *( T + 7/3600 ) Km , which we have already assumed as X km. 


204*T Km = 200 *(T+ 7/3600 ) KM

204 T = 200 T + 200 x 7/3600
4 T = 7/ 18
T= 28/18 Hrs. = 1.5 Hrs. 

Distance covered by the first car in 1.5 Hrs. at the speed of 204.2 Km/Hr  204.2 x 1.5= 306.30 Km

Another problem
Two train starts , one from station A towards station B at morning 8:00 AM and reached at station B at 10:30 AM. 
Another train starts from station B at 9:00 AM and reached station B at 12:00 noon. When both the trains will meet? 

Solution

Let the distance between the stations A and B be X km. and let after a time T    both the trains meet at a same point. 
Speed of train A is ( X /2.5 ) Km/hr and speed of train B is ( X/3) Km/hr
So in time T train A travels (X/2.5)*T Km. 
and in time T train B travels (X/3)* T Km.

Now , we know that to total distance is  X Km.   

(X/2.5)*T +(X/3)*T = X
or, XT/2.5 + XT/3= X
or,X(T/2.5+ T/3)= X
or, T/2.5+ T/3= 1
or,( 3T +2.5T)/7.5= 1
or,5.5 T= 7.5
or,T = 7.5/5.5 Hr= 15/11 Hr= 

One simple mathematics

Factorise
  4 X2 - 12 X + 9 = 0

OR, (2X)2 - 2. 2X. 3 + (3)2 = 0
OR, (2X -3)(2X-3)
OR, X = 3/2

PROBLEM

3 ^(X-Y) = 27 = 3 ^{3  ______________________}1

3^(X+Y)= 243= 3 ^{5________________________}2

OR,    X- Y = 3

           X+ Y= 5   OR , 2 X      =  8   OR  X = 4    When  X = 4 , Y = 1

Other  problem

 Find value of    3 * square root of 5 *  5 * square root of 3  

Let,  3 * square root 5 * 5 square root 3 =  X

So , X ² =  9 *5 *5*3

Or, X ² =  3*3 *5*5*3

Or, X = 3*5* square root 3

Or, 15 square root 3

Now, if the  integers are   3 square root 5 *  5 Square root 3

Let it is X ,

So X =  3 square root 5 * 5 square root 3

Squaring both sides,   X ² = 45 * 75

Or , X = 15 square root 15