Affects on constant and average velocity if Emily stops driving her effing car for 22.0 minutes...?

Question

"Except for a 22.0 min rest stop, Emily drives with a constant velocity of 89.5 km/h, north. How long does the trip take if Emily's average velocity is 77.8 km/h, north?"

Well, I'd much rather the question read, "Emily's car is blue. Eat it with ketchup, please. How old is your doorknob?" Of course, the present question makes just about as much sense. I've recently asked another question and feel quite stupid for it, but this one's been confusing me for the past half-hour or so. :( Any chance of help?

Answer 1

This question requires you to create two equations, based upon the equation:
d = vt (distance equals velocity multiplied by time)

For our equations, we'll say that "t" is the time for the trip in hours. "t - 22/60" is the time for the trip without the rest stop, in hours.

The first equation is for the trip without the rest stop.

d = 89.5 (t - 22/60)
d = 89.5 t - 1969/60 (equation #1)

The second equation is for the trip with the rest stop.

d = 77.8 t (equation #2)

Now combine these two equations by subtracting equation #2 from equation #1.


0 = 11.7 t - 1969/60
11.7 t = 1969/60
t = 1969/(60 * 11.7)
t = (1969/702) hours

So now we know the time for the trip with the rest stop - 1969/702 hours. This is approximately equal to 2.805 hours. Restated in more human understandable terms, Emily's trip was approximately 2 hours 48 minutes long.

Answer 2

Ok, the 22 minutes lowered her otherwise screamin' fast velocity of 80.6 km/h all the way down to 77.8 km/h.

Her actual time spent moving was, let's say, T. So for distance D,

D/T = 80.6 km/h
and
D/(T+(22/60)) = 77.8 km/h

There--2 equations with two unknowns. Solve for one of them and plug into the other and you'll get an answer for T. Be sure to add the 22 minutes to T because the question was "how long does the trip take?" which would include her rest stop. Cheezz, what was she doing for 22 minutes?! But that's another question.

Answer 3

Aalksdfjlakdjg. I'm in the same boat, with problems almost exactly the same as yours. *sigh* My homework makes me want to sit down in the floor crying and flubbing my lips.

I like your alternative question. I wish I could use that as an answer. Unfortunately, I don't think my professor would appreciate it. He doesn't have much of a sense of homour outside of his own jokes.

I do have the formula to work it with, though! I think. Give me a moment to hunt it down in my notes, and I'll edit here.

Edit: Aaand it looks like two people hit 'submit' before I did. Ah well, at least you got the answer. ;) Good luck on the rest of your homework!

Answer 4

you need to know how far she is going. you don't know time, because there is no end to the trip.