Question 1118151
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Let the speed of the slower train be x; then the speed of the faster train is x+25.<br>
The wording of the problem as given:
"the faster train takes 2 hours less to travel 150km than the slower train takes to travel 125km"<br>
Translation into a mathematical sentence that can be turned directly into an equation:
"the time it takes slower train to go 125 km is 2 hours more than the time it takes the the faster train to go 150 km"<br>
Translation (since time equals distance divided by rate):<br>
{{{125/x = 150/(x+25) + 2}}}<br>
If an algebraic solution is not required, I would definitely use logical trial and error to solve the problem.  Since the difference in times is exactly 2 hours, the numbers in the problem have to be "nice" numbers.  Looking at the equation, my first guess (because of the "125/x") would be x = 25 -- and it works:<br>
125/25 = 5; 150/50 = 3; 5-3 = 2<br>
If an algebraic solution is required, then I would multiply the whole equation by the least common denominator of all the fractions:
{{{125/x = 150/(x+25) + 2}}}
{{{125(x+25) = 150x + 2x(x+25)}}}
{{{125x+3125 = 150x+2x^2+50x}}}
{{{2x^2+75x-3125 = 0)}}}
{{{(x-25)(2x+125) = 0}}}
{{{x = 25}}}<br>
Factoring that quadratic equation would have been very time-consuming if I hadn't already known the answer....