SOLUTION: hi To travel 816km train A takes 9 hours more than train B. if the speed of train A is doubled, it takes 4 hours less than train B . what is the speed of train B. thanks

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Question 1150350: hi
To travel 816km train A takes 9 hours more than train B. if the speed of train A is doubled, it takes 4 hours less than train B .
what is the speed of train B.
thanks
Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

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:

Let A = speed of train A
Then 2A = speed of train A if its speed is doubled
Let B = speed of train B

Then

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

(1) The time train A takes to go 816km is 9 hours more than the time train B takes to go 816km:

(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:

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.

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.

I leave it to you to finish the problem by whatever method you choose.

If a formal algebraic solution is not required, then a solution is easily obtained using logical reasoning and a bit of simple mental arithmetic.

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.

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.

That means train B takes 26-9 = 17 hours to make the trip.

And that means the speed of train B is 816/17 = 48km/h.