train overtake man distance formula

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jeffreyleo

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Question is a 240 metre long train overtake a man walking at 3km/hour in the same direction. It takes train 9 seconds to overtake the man. Ask what is train's speed.

suppose train speed is x km/hour, then

The standard answer is distance travelled=train length 0.24=(x-3)*9/3600, and answer is 0.24=9x/3600-27/3600. 864=9x-27, x=99

However, as the man is also walking, shouldn't we add up whatever the distance man walks and put the formula as 0.24+3*9/3600=(x-3)*9/3600, and the answer becomes 864+27=9x-27, 9x=918, x=102.

Thanks for your help
 
jeffreyleo said:
Question is a 240 metre long train overtake a man walking at 3km/hour in the same direction. It takes train 9 seconds to overtake the man. Ask what is train's speed.

suppose train speed is x km/hour, then

The standard answer is distance travelled=train length 0.24=(x-3)*9/3600, and answer is 0.24=9x/3600-27/3600. 864=9x-27, x=99

However, as the man is also walking, shouldn't we add up whatever the distance man walks and put the formula as 0.24+3*9/3600=(x-3)*9/3600, and the answer becomes 864+27=9x-27, 9x=918, x=102.

Thanks for your help
Click to expand...
Assume that the origin is fixed to the ground and the speed of the train is 'v'. Then:

(0.24 + 3* 9/3600) / v = 9/3600

Solve for 'v' .
 
jeffreyleo said:
Question is a 240 metre long train overtake a man walking at 3km/hour in the same direction. It takes train 9 seconds to overtake the man. Ask what is train's speed.

suppose train speed is x km/hour, then

The standard answer is distance travelled=train length 0.24=(x-3)*9/3600, and answer is 0.24=9x/3600-27/3600. 864=9x-27, x=99

However, as the man is also walking, shouldn't we add up whatever the distance man walks and put the formula as 0.24+3*9/3600=(x-3)*9/3600, and the answer becomes 864+27=9x-27, 9x=918, x=102.

Thanks for your help
Click to expand...
My first question is, what do you mean by "standard answer". Where did that come from, and is any explanation given?

What we can do is to check the meaning of that equation, and then of yours; and then check the results in each case.

The equation 0.24=(x-3)*9/3600 says that the distance the train moves in 9 seconds relative to the man (namely, the train's length) is equal to 9 seconds times the train's speed relative to the man's. This is all appropriate. They (whoever "they" are) are using a frame of reference moving with the man.

The equation 0.24+3*9/3600=(x-3)*9/3600 says that in 9 seconds, the train moves its length plus the distance the man has moved (in a fixed frame of reference), with the train moving at its relative speed, x-3. This is mixing two ways of thinking. If you want to use the fixed frame of reference, then you need to use the absolute speed, x. The appropriate equation is 0.24+3*9/3600=(x)*9/3600.

If you examine these equations, you should see that the corrected equation is equivalent to "theirs".

Checking your answer of 102 km/h, we see that in that time the train has moved 102*9/3600 = 0.255 km, which is 15 m more than its length; but the man has moved 3*9/3600 = 0.0075 km = 7.5 m; the train has gone 7.5 m past the man.
 
@jeffreyleo

This is your first post. Please read the post entitled Read Before Posting. There you will see that we ask you to QUOTE EXACTLY AND COMPLETELY the problem you were given.

Let’s see why your answer is wrong.

Let w = the speed of the man in kilometers per hour.
Let x = the speed of the train in kilometers per hour.
Let y = the time in hours for the train to pass the man.
Let z = the length of the train in kilometers.

One way to solve this is to consider the total distance travelled by the train, namely [imath]z + wy[/imath]. You are correct in that conclusion. Therefore the train’s speed is [imath]x = \dfrac{wy + z}{y}.[/imath]

Another way to solve this is by relative speed. The train is moving (x - w) faster than the man. How much faster is the man moving than himself? (w - w). So using these relative speeds the man is not moving at all. Then we go

[math](x - w)y = z \implies x - w = \dfrac{z}{y} \implies x = w + \dfrac{z}{y} = \dfrac{wy + z}{y}.[/math]
Same answer, two different approaches.

What you cannot do is divide the total distance travelled by the train by how much faster it is going than the man.

EDIT: Dr. Peterson is looking inside my mind again. Subhotosh, tell him to stop.
 
Thank you so much for all your detailed reply. What happened is when I search for the answer on google, I only find the formula, and no any reason behind the formula.

Thank you all. I now have more confidence when explaining such questions to my kid.
 
You should get your child to use this site on his or her own for two reasons.

One is to develop the child’s self reliance.

Second is that the helpers here frequently use different approaches, which maximizes the chance of finding an approach that matches the kid’s natural mode of thinking.
 
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