The distance between two places is 120 km. A car travelling at a certain speed can cover the distance in 2 hours 30 minutes. By how many km/h should the speed of the car be increased for it to take 30 minutes less to cover the distance? Don't spam!!
Step by step explanation is needed..

Distance between two places=120 km

Step-by-step explanation:

Time= 2 hrs 30 min

       =(2*60)min+30min

       =120min+30min

       =150min=150/60 hr

        = 5/2 hr

Speed = distance /time

          = (120/5/2)km/hr

          =(120×2/5)km/hr

          =(240/5)km/hr

          = 48 km/hr

New time = 2 hr 30min-30min

               = 2hr

Distance =120km

Speed  = Distance /time

           =120/2 km/hr

           = 60 km/hr

Increase in speed=(60-48)km/hr  

                            =12km/hr

Another way to show :

Distance = 120km

speed=Distance/time

=120/2.5=48 km/hr

New speed=120/2=60 Km/hr

change inspeed=60-48=12km/hr

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: