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
On
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
On
The unit they are asking for is miles per hour so you need to know:
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.
On
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 $$ v = \frac{s}{t} = \frac{90 \, \text{miles}}{11.25 \,\text{h}} = 8 \frac{\text{miles}}{\text{h}} $$
By definition we have
$$v=\frac d t = \frac{90}{11.25}=8$$
note indeed that $15$ min = $\frac14$ h = $0.25$ h.