SOLUTION: A train travels 300km at a constant speed. If the speed had been 5km/h faster, the jounery would have taken 2 hours less. Find the speed of the train

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Question 1034622: A train travels 300km at a constant speed. If the speed had been 5km/h faster, the jounery would have taken 2 hours less. Find the speed of the train
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28d=300%2Ch=2%2Cs=5%2Cr=knownActualRate%2Ct=knownActualTime%29


                RATE           TIME         DISTANCE

ACTUAL           r             t            d

HYPOTH          r+s            t-h          d


The basic travel rates rule is RT=D to relate rate, time, and distance.
Form the equations for the system and solve for the unknown variables.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Your equation is 

300%2Fu+-+300%2F%28u%2B5%29 = 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%5E2+%2B+10u+-+1500 = 0,   or

u%5E2+%2B+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.

Answer.  The train'speed is 25 km%2Fh.