An express train makes a run of 240 km at a certain speed. another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr

116.9 km/hr

Step-by-step explanation:

Let the speed of the express train be s and the time required by that train to cover 240 km be t.

Since distance = rate times time,

rate = distance / time

                                                            240 km

and so, for the express train, rate =

                                                                   t

To solve this problem, find the rate of the express train first.

                                                                 240 km

For the other train, rate - (12 km/hr) =

                                                                     t - 1

Substituting (240 km)/1 for rate in the second equation results in:

240 km       12 km         240 km

- =

    1 hr            1 hr              t - 1

Simplifying the left side, we get:

 228 km       240 km

=

     1 hr              t - 1

Note that if we multiply 228 km by 1.053, we get 240 km.

Let's multiply both numerator and denominator of the left side of the above equation by 1.053:

 240 km         240 km

=

  1.053 hr           t - 1

Then t - 1 = 1.053, and t = 2.053 (hours)

We already know that the speed of the first train is

            240 km

rate =

                   t

and we now know that t = 2.053 hrs.

Thus, the rate of the express train is

            240 km

rate = =  116.9 km/hr

             2.053 hrs                                                       t

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!