<PRE><B>Question 550389</B>
n express train makes a run of 240 km at acertain 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.
:
let s = speed of the express
then
(s-12) = speed of the other train
:
Write a time equation, time = dist/speed
:
Other train time - Express train time = 1 hr
{{{240/((s-12))}}} - {{{240/s}}} = 1
Multiply by s(s-12)
s(s-12)*{{{240/((s-12))}}} - s(s-12)*{{{240/s}}} = s(s-12)
Cancel the denominators and you have
240s - 240(s-12) = s^2 - 12s
:
240s - 240s + 2880 = s^2 - 12s
combine like terms and arrange as a quadratic equation
0 = s^2 - 12s - 2880
you can use the quadratic equation but this will factor to
(s+48)(s-60) = 0
s = 60 km/hr is the the express train
:
:
check this by finding the times of each
240/48 = 5 hrs
240/60 = 4 hrs
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