speed and distance question

Topic:Speed and Distance

Speed is the rate of motion, or equivalently the rate of change of distance.

If the speed of an object is given ,We can find the Distance and similarly ,if the speed has given we can find the speed as well .

Here is an example problem ...
Question : A train travels 360km at a uniform speed. If the speed had been 5km/h more it would have taken 1 hour less for the same journey. find the speed of the train?

 
Let the speed of the train be x km/hr.
Distance travelled by the train =360 km
                Distance     360
So time taken =  --------- = ----
                 speed       x
Now the new speed =(x+5)km/hr.

                        360
So the time taken will be------ hr
                        x+5

Now the new time is 1 hour lesser.

So the equation will be

    360          360
  -------  -  ------- = 1 
     x            x+5
Making the denominator equal

  360(x+5)    360x
 --------- - ------- = 1
      x       x+5
  360x+1800-360x
  ---------------  = 1
      x(x+5)
1800 = x(x+5)

 1800 = x2+5x

Quadratic formula:
        -b+√b2-4ac
 x= ----------------------
           2a

Here a=1,b=5,c=1800

      -5+√52-4*1*1800
So x= --------------------------
               2*1
       -5+√25+7200
     = -------------
            2
        -5+√7225
     = ------------
           2
         -5+85
     =   --------
            2
So   x= 40 km/hr is the Answer

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Problem on Distribution in Algebra

Topic :- Distribution property


distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example:


Question:- How to Solve 2(3x+5)=5x-11


Ans:-


Step 1:- Use the distribution rule to solve 2(3x+5)

2*3x + 2*5

=6x+10

So,6x+10=5x-11


Step 2:- Subtract 5x from both sides


6x+10=5x-11
-5x -5x
----------------------------
x+10= -11

Step 3:- Subtract 10 from both sides


x+10= -11
-10 -10
----------------------
x = -1

So x= -1 is the Answer.


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