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I'm at a really loose end - I just can't seem to grab some fundamentals of Speed Distance Time.

Can someone explain to me how they discover the answer to the following equipped with steps on how to figure out. I really cannot remember the process in how to do so since I left school.

If your journey lasts 11 hours and 15 minutes what speed are you travelling at if you cover 90 miles?

I know the answer is 8MPH but I'm not sure in how to reach the answer.

Thanks

K

mvw
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karlb123
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  • Unit analysis is helpful here. You are told that the journey is $11.25\ \text{hr}$ long, and that it covers a distance of $90\ \text{mi}$. Your answer is a speed, in miles per hour. "Per" means divide, thus the answer is $x\ \frac{\text{mi}}{\text{hr}}$. You know that the units have to be $\frac{\text{mi}}{\text{hr}}$, so divide distance by time to get speed. – Xander Henderson Aug 06 '18 at 01:12
  • @karlb123 Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details here https://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work – user Sep 06 '18 at 23:07

4 Answers4

3

The unit they are asking for is miles per hour so you need to know:

  1. How many miles they covered
  2. How many hours it took.

Once you know these two, you need to divide the miles by the hours.

The answer to 1 is given in the question - they covered $90$ miles.

The answer to 2 is slightly hidden, the question gives $11$ hours $15$ minutes, which is the same as $11$ hours and a quarter of an hour, or $11.25$ hours.

Now all you need to do is $$\frac{90}{11.25}=\frac{90}{(\frac{45}{4})}=\frac{4\cdot90}{45}=4\cdot2=8$$ to get the answer you were looking for.

Rhys Hughes
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By definition we have

$$v=\frac d t = \frac{90}{11.25}=8$$

note indeed that $15$ min = $\frac14$ h = $0.25$ h.

user
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  • @jonaslenz - thank you for both your input it is very well received. I think the issue is, is that I'm using a pen and paper with no access to calculator. Any easier way to simplify this? – karlb123 Aug 05 '18 at 21:01
  • We have $$8\cdot 11.25=8\cdot (10+1+0.25)=8\cdot 10 + 8\cdot 1 + 8 \cdot 0.25=80+8+2=90$$ therefore $90/11.25=8$. – user Aug 05 '18 at 21:03
  • Or use that https://www.wolframalpha.com/input/?i=90%2F11.25 – user Aug 05 '18 at 21:04
  • @gimusi your first comment doesn't help in my opinion as the OP won't know that $8$ is a correct answer and so division by reverse multiplication isn't a good option. (This looks to me like a homework question where the OP has seen the answer but been confused by how to get there) – Rhys Hughes Aug 05 '18 at 21:07
  • @RhysHughes Yes maybe you are right, your way is indeed much clear for this kind of explanation. I've given a way to check since he already knows the result. – user Aug 05 '18 at 21:09
  • @RhysHughes exactly that! Thanks - I'm actually studying for an interview next month which involves SDT in calculations – karlb123 Aug 05 '18 at 21:09
  • @karlb123 Notice that the $.25$ on a number with no other decimals guarantees that the number is of the form $\frac x4$, so here multiplying $11.25 \times 4$ to get $45$ shows that $11.25=\frac{45}{4}$, and so you have $\frac{90}{(\frac{45}{4})}$. Then use that $\frac{a}{(\frac bc)} =\frac{ac}{b}$, as my answer does. – Rhys Hughes Aug 05 '18 at 21:14
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As velocity is given in miles per hour, let's just calculate this. You needed 11hrs 15min=11,25hrs for 90 miles. So in 1hr one has travelled $90/11,25=8$ miles. So the velocity is 8MPH

Jonas Lenz
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If your journey lasts 11 hours and 15 minutes what speed are you traveling at if you cover 90 miles?

Velocity is the time derivative of the position $s(t)$: $$ v(t) = \frac{d}{dt} s(t) $$

Speed is the magnitude of the velocity.

To solve your task we assume the simple case of constant velocity. In this case we have: $$ s(t) = v t $$ where we used the further simplifications that we have position $s=0$ at time $t=0$, thus $s(0) = 0$.

The last hurdle is to use proper units. $$ t = 11 \,\text{h} \, 15 \,\text{min} = 11.25 \,\text{h} $$ so $$ v = \frac{s}{t} = \frac{90 \, \text{miles}}{11.25 \,\text{h}} = 8 \frac{\text{miles}}{\text{h}} $$

mvw
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