Question 1150350
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Algebraically, there are many ways to set up the problem.  Without trying to overthink the problem, it could be set up directly from the given information as follows:<br>
Let A = speed of train A
Then 2A = speed of train A if its speed is doubled
Let B = speed of train B<br>
Then<br>
816/A = time train A takes to go 816km
816/B = time train B takes to go 816km
816/(2A) = time train A takes to go 816km if its speed is doubled<br>
(1) The time train A takes to go 816km is 9 hours more than the time train B takes to go 816km:<br>
{{{816/A = 816/B+9}}}<br>
(2) The time train A takes to go 816km if its speed is doubled is 4 hours less than the time it takes train B to go 816km:<br>
{{{816/(2A) = 816/B-4}}}<br>
There are two equations in A and B which you can solve to find the speed of train B; you can solve them by any method you choose.<br>
Since the two equations contain the term 816/B, I would use substitution to get an equation in only A; then after solving that equation for A I can use that value of A in either of the original equations to find B.<br>
I leave it to you to finish the problem by whatever method you choose.<br>
If a formal algebraic solution is not required, then a solution is easily obtained using logical reasoning and a bit of simple mental arithmetic.<br>
At its normal speed, train A takes 9 hours more than train B to make the trip; when its speed is doubled, train A takes 4 hours less than train B.  So doubling the speed of train A shortens the trip by 13 hours.<br>
When the speed of train A is doubled, the time required for the trip is cut in half.  Since doubling the speed saved 13 hours, train A at its normal speed takes 26 hours for the trip.<br>
That means train B takes 26-9 = 17 hours to make the trip.<br>
And that means the speed of train B is 816/17 = 48km/h.<br>