Question 1196420
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There are two ships travelling from dumaguete to cagayan de oro differ in average speed by 10kph. 
The slower ship takes 3 hours longer to travel a 240km route than for the faster ship 
to travel a 200km route. Find the speed of the slower ship. 
As a navigator, you are assigned to measure the speed of the slower ship.
Hint:construct an equation with time t as the variable
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<pre>
Let x be the speed of the slower ship, in kilometers per hour.

It covers the distance of 240 km in  {{{240/x}}}  hours.


The faster ship has the speed of (x+10) km/h and covers 200 km in  {{{200/(x+10)}}}  hours.

We are given the time {{{240/x}}}  is 3 hours longer than time {{{200/(x+10)}}}.



So we write this "time" equation


        {{{240/x}}} - {{{200/(x+10)}}} = 3  hours.


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    |    As soon as you got it, the setup is complete.  |
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To solve the equation, multiply both sides by common denominator x*(x+10).
You will get

    240*(x+10) - 200x = 3x*(x+10)

    240x + 2400 - 200x = 3x^2 + 30x

    3x^2 - 10x + 2400 = 0


Solve this quadratic equation using the quadratic formula

    {{{x[1,2]}}} = {{{(10 +- sqrt(10^2 + 4*3*2400))/(2*3)}}} = {{{(10 +- sqrt(28900))/6}}} = {{{(10 +- 170)/6}}}.


There are two roots, one is 30, the other is {{{-160/6}}} = -{{{80/3}}}.


We reject the negative root and accept the positive root.


So, the <U>ANSWER</U> is 30 km/h for the slower ship.


<U>CHECK</U>.  Time for the slower ship is  {{{240/30}}} = 6 hours;  time for the faster ship is {{{200/40}}} = 5 hours.

           The difference of times is 8-5 = 3 hours, confirming the answer.
</pre>

Solved and thoroughly explained.