Question 198348
A fast train takes three hours less than the slow train for a journey of 600
 km. If the speed of slow train is 10km/hr less than that of fast train.
Find the speed of the two trains.
:
Let s = slow train speed
then
(s+10) = fast train
:
Write a time equation: Time {{{dist/speed}}}
;
Slow train time - Fast train speed = 3 hrs
{{{600/s}}} - {{{600/((s+10))}}} = 3
Multiply each term by s(s+10); results
600(s+10) - 600s = 3s(s+10)
:
600s + 6000 - 600s = 3s^2 + 30s
:
Arrange as a quadratic equation, (600s's cancel)
3s^2 + 30s - 6000 = 0
Simplify, divide  by 3
s^2 + 10s - 2000 = 0
Factors to
(s = 50)(s - 40) = 0
positive solution
s = 40 km/hr speed of the slow train
then
50 km/hr speed of the fast train
:
:
Check solution by finding the time difference
600/40 = 15 hrs
600/50 = 12 hrs
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difference 3 hrs