Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Distance Problems -Help!

I need help with these distance problems. They are so annoying and I find them a bit difficult. Also, please show work!

(1) A pilot plans to make a round trip flight lasting 2.5 hours. How far can the pilot plan to go if the rate going is 480 kilometers per hour and the rate returning is 320 kilometers per hour?

(2) Sherry drove 80 miles from her home to City A. On the way home (same route), she drove 12 miles per hour faster than she did on the way to City A. If she arrived home in

of the time she took on the way to City A, how many minutes did it take for her to drive from home, to City A?

(3) It takes a boat 2 hours less to travel downstream than to travel back upstream. If the round trip is 100 miles and the boat travels 5 miles per hour faster to the downstream than to the upstream, how fast did the boat travel to the upstream?

(4) A jet airline takes 1.2 times as long to fly from Paris, to New York (3,600 miles) as to return. If the jet cruises at 550 miles per hour in still air, what is the average rate of the wind blowing in the direction of Paris from New York?

This next one, I just need verification that I did it correctly!

(1) Two planes travel at right angle to each other after leaving the same airport at the same time. One hour later, they are 260 miles apart. If one plane travels 140 miles faster than the other, what is the rate of each plane?

Let a be the speed of the slower plane. So, from Pythagorean Theorem, we have

.

Expanding and simplifying gives

That factors into whatever that factors into to, and we choose the positive solution of the two solutions.

Is that correct? I still need to factor, but other than that, I'm good!

Thank you for your time and effort (more like effortless) on this post. Have a nice day!

P.S This is my

post! Which simplifies into

post!

Last edited by evene (2016-02-18 14:38:29)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Distance Problems -Help!

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Distance Problems -Help!

What a weird number...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Distance Problems -Help!

That is what I thought too.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Distance Problems -Help!

So, I figured out the first problem and the fourth problem. Now, I just need to know the second one.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Distance Problems -Help!

1. Let x be the distance we are looking for, t1 the time to go and t2 the time to return.
x = 480.t1 so t1=x/480
x = 320.t2 so t2=x/320
t1+t2 = 2,5 hours
so:
x/480+x/320 = 2,5 so
x=480 km

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Distance Problems -Help!

2. Let S = 80 miles be the distance from Sherry’s home to City A, V1 her speed when driving from her home to A and V2 her speed when returning home.
Also let t1 be the time to go and t2 the time to return.
V2=V1+12
t2=5/6.t1
V1.t1=80
(V1+12).5/6.t1=80
By dividing both parts we get:
V1/(V1+12)=5/6
So V1=60mph and t1=80/60 hours = 80 minutes.

I guess you can now easily solve Nr. 3.

If you still need help, let me know.

Last edited by anna_gg (2016-02-20 05:24:10)

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: Distance Problems -Help!

They are very simlpe (straightforward applications of Algebra) the first and second problems can be solved as provided by "anna_99" and you have mentioned above that you have solved the fourth problem. About the solution of the extra problem ,which you displayed alon, your solution is correct, and you can factorize the polynomial as follow:

or

Now you made a little mistake in your reasoning about the negative value of the velocity since you can ,in fact, use the negative or the positive values!! Because velocity is a vector so it has a magnitude and direction (not like a scalar quantity ,as the distance, which has a magnitude only) so in general the answer depends on the directions which you take as positive. But in this case they ask only for the "rate of change" hence you can use any value (negative or positive) for calculation and then drop the sign (you will get the same answers).
To solve problem number "3" let

to be the upstream travel while

denotes the downstream travel, so from the provided data we have:

But we know also that:

Now since the rquired value is the speed (the magnitude) of the upstream travel and the problem discribes travel in both directions as if they were parallel, we will take the positive value and discard the negative (the problem has been transulated into the above equations with this idea in mind). Therefore:

or

Hence the required answer is

mi/h

Q.E.D

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Distance Problems -Help!

Just for the record, I have a hard time understanding Speed and Distance problems and setting up equations.

Thanks anna and Grantingriver.

Grantingriver, this is for you: Doesn't Q.E.D mean quod erat demonstratum, which translates into "which was to be proven"? If so, then what are we proving?

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: Distance Problems -Help!

Well. It is maybe more apropriate in this satuation to say "Q.E.F" (quod erat  faciendum) instead, which means "which had to be done" but technically if you provide a proof for something you supply statements (premises) that entail logically another statement (conclusion) and in deed we have done the same thing, but you are right it is better to say "Q.E.F" in this case. Thank you for your remark.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Distance Problems -Help!

You take Latin too?