Question 1034622
.
A train travels 300 km at a constant speed. If the speed had been 5 km/h faster, the joinery would have taken 2 hours less. 
Find the speed of the train.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Your equation is 

{{{300/u - 300/(u+5)}}} = 2.

where "u" is unknown train' speed.

To solve it, multiply both sides by u*(u+5) to get rid of the denominators. You will get

300*(u+5) - 300u = 2u*(u+5),   or

{{{2u^2 + 10u - 1500}}} = {{{0}}},   or

{{{u^2 + 5u - 750}}} = {{{0}}}.

Factor left side

(u+30)*(u-25) = 0.

The roots are u = 25 and u = -30.

Only positive u = 25 fits the condition.

<U>Answer</U>.  The train'speed is 25 {{{km/h}}}.
</pre>