Question

Please HELP! :)mr. Duncan traveled to a city 180 miles from him home to attend a meeting. Due to car trouble, his average speed returning was 13 miles less than his speed going. If the total time for the road trip was 7 hours, at what rate of speed did he travel to the city? (round to nearest tenth)

Answer 1

Formula is d=rt. Make two equations and set them equal to each other to find the rate, and then find the average, which is the first plus the second divided by 2

Answer 2

so 180=r7 so 173/2..so 86.5?

Answer 3

distance equal rate x time
there are two equations we can use here. Going and coming.

let t= time going
let 7-t= time coming
let x = rate going
let x-13 = rate coming

distance going and coming is 90 (180/2)
so remember d=rt
coming
90 =(x-13)(7-t)
going
90 = xt
solve this system of equations.

Answer 4

wait, did you just solve it? ha, i'm confused. That all kind of makes sense. I just am not sure what the last step is?

Answer 5

@junwagh
I think u r making a mistake
The question says "Duncan traveled to a city 180 miles from his home"
This means one way distance is 180 miles and not 90 miles

Answer 6

I set up the problem. We set up two equations using d =rt. One for going and one for coming. Then you solve that system of equations. I won't do that for you, the hard part is setting up the equation.

90 = xt
90 = (x-13)(7-t)

Answer 7

yep the total distance is 180

Answer 8

yes the total distance is 180, which means the distance going there is 90 and the distance coming back is also 90.

Answer 9

oh wait mi bad
lol replace 90with 180 then.

Answer 10

The total distance has to be 360 miles as the "city is 180 miles from his house" so he has to go 180 miles and come back 180 miles

Answer 11

it says from his house to attend the meeting he drove 180 miles.. hmm yeah. you might be right. Ahh. does anyone have an answer. Now all the numbers are confusing me. want to make sure I know how to solve with the last steps

Answer 12

someone suggested 59 mph. anyone else get that?

Answer 13

Okay here is how u do it
Let his speed while going = x miles /hour
Then his speed while coming back = (x-13) miles/hr
Distance each side is 180 miles
we know distance = speed x time or time = distance/speed
So time taken while going = 180/x and
time taken while coming back = 180/(x-13)

Answer 14

Now the total time taken is 7 hours. This means
(180/x) + 180/(x-13) = 7
or
180(x-13) + 180 (x)
------------------ = 7
x(x-13)

Simplifying the above we get

180x - 2340 + 180x = 7 (x^2 - 13x)

Answer 15

so how do we find the rate of speed he traveled to the city Thank you for writing that all out for me. I just want to make sure I put in the correct answer.

Answer 16

DOes anyone have a final answer for this problem? I have been trying to work it out for over an hour so I would really appreciate any help with the solution.

Answer 17

what answer did you get?

Answer 18

Further this gives us 360x - 2340 = 7x^2 - 91x
Further simplifying we get
0 = 7x^2 - 91x - 360x + 2340 or
7x^2 - 451x + 2340 = 0
This is a quadratic eqn. U can resolve it and get value of x

Answer 19

59 mph

Answer 20

that got me 2 solutions. 5.69 and 58.74...Is there a way to make this into 1 answer?

Answer 21

maybe i'll just try 58.74.. Think this will be right?

Answer 22

i got it right. THanks everyone

Answer 23

yes it is 59.1 mph

Answer 24

58.74 is correct as your speed cannot be 13 miles less than 5.69!!

Answer 25

i actually did 58.7 and this was correct.

Answer 26

It is a long winded question for sure

Answer 27

http://www.mathsisfun.com/quadratic-equation-solver.html
you can use that to solve your quadratic equation exactly. Just plug in your values.

Answer 28

x=speed out, t=time out, x-13=speed back, 7-t=time back
{x t == 180, (x-13)*(7-t)==180}
{{x->5.69119,t->31.6278},{x->58.7374,t->3.06449}}
Using second pair of x, y values.
Speed, Time Out = {58.7374,3.06449}
Speed, Time Back = {45.7374,3.93551}

Answer 29

@robtobey
how did u get th values {{x->5.69119,t->31.6278},{x->58.7374,t->3.06449}}

Answer 30

Running the Mathematica Solve function:

Solve[ { x t == 180, (x-13)*(7-t)==180}, {x,t} ]

Answer 31

The syntax is somewhat weird. Those are, two consecutive = symbols.

Answer 32

I am not familiar with this...
Anyway thanks for th reply!!

Answer 33

\[\left\{x\to \frac{1}{14} \left(451+\sqrt{137881}\right),t\to \frac{1}{26} \left(451-\sqrt{137881}\right)\right\} \]
The above is the actual output returned from Mathematica for the x, t, values used. Placing "//N" at the end converts to decimal numbers.

Answer 34

Is this Mathematica some program to calculate answer or is it a mathematical theory like quadratic equations etc
The answer seems like solution to the quadratic eqn

Answer 35

I calculated using the formula
-b +- root b^2 - 4ac
x = ---------------------
2a

Answer 36

Harkirat, mathematica is a mathematics software tool which helps you do calculations.

Answer 37

OK!!??!! Thanks dhatraditya !! Is it free and available on net??

Answer 38

Mathematica is a very large application system. About 3Gb of data to install it. It has been years in development and is mathematically very comprehensive in scope.

It is about $2500 to a the common mom and popper who belly up to the cash counter to buy. For students and teachers they almost give it away. On the order of $125 one time cost as long as the student remains a student. The teachers probably would not allow it to be used in a class test but it will always show the correct answers for home work as long as the input is correct.

If you give me a minute I'll find their web site.

Answer 39

sure , thanks

Answer 40

The Mathematica site is:

http://www.wolfram.com/

I just purchasee Mathematica version 8 Home edition. It cost me about $280 for a box edition delivered to California. By the way the installation comes on a DVD not a CD.

Because of low price, the use of the Home is very restricted. For instance I can not use in to make any money.

Answer 41

Thanks robtobey, I am in India and this is beyond my reach

Answer 42

They may ship to India or have an agent there.

I have to break off now. Been good talking to you.

Adios.

Answer 43

thank friend n bye till we chat again