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January 11th, 2017, 08:54 PM   #1
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Year 10 Motion problem

Question:

A motor cyclist makes a trip of 500km. If he had increased his speed by 10km/h, he could have covered 600km in the same time. What was his original speed?

Answer: 50km/h

I tried solving it by using d=st

st + t(s+10) = 500 + 600
st + st + 10t = 1100
2st + 10t = 1100

I think I'm doing it wrong though. Could someone help me?

Last edited by skipjack; January 12th, 2017 at 04:29 AM.
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January 11th, 2017, 10:06 PM   #2
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The key here is that in both cases, the time is the same.

So for the first case, we have the following,
$\displaystyle
500 = \frac{1}{2}v t$

And so, $\displaystyle t = \frac{1000}{v}$.

Now if we follow a similar procedure, this time having a known value for t, we have,

$\displaystyle 600 = \frac{1}{2} (v + 10) * \frac{1000}{v}$

$\displaystyle 1200 = \frac{1000 \cancel{v}}{\cancel{v}} + \frac{10000}{v}$

$\displaystyle (1200 - 1000)v = 10000$

$\displaystyle \therefore v = 50km/h.$

Note that I have been sloppy with labeling my units here. Always remember what units you are working with!

Last edited by skipjack; January 12th, 2017 at 03:51 AM.
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January 12th, 2017, 04:27 AM   #3
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Quote:
Originally Posted by pianist View Post
I tried solving it by using d=st . . .
As distance increase = (speed increase) * time, time = 100km/(10km/h) = 10h,
and so the original speed = 500km/(10h) = 50km/h.

If you prefer to use your variables, you can write that as shown below.

Subtracting st = 500km from (s + 10km/h)t = 600km gives (10km/h)t = 100km, and so t = 10h.
Hence s = 500km/t = 50km/h.
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January 12th, 2017, 05:51 AM   #4
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I understand your solution, but in my textbook there is an example preceding the question. In the example, it adds the variables instead of subtracting it. Is there a way to do it similar to the example method or not?
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January 12th, 2017, 07:10 AM   #5
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Quote:
Originally Posted by pianist View Post
I understand your solution, but in my textbook there is an example preceding the question. In the example, it adds the variables instead of subtracting it. Is there a way to do it similar to the example method or not?
That's a different problem entirely, so it has a different solution. Don't compare them in terms of "adding things" or "subtracting things" because you shouldn't work like that. If you stick to the formulas, you'll be fine.
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