Math Word Problem help?

Question

Here is a problem that i need help on, I dont want just the answers, i need the work, and please walk me through it

In going between two floors a man takes the freight elevator up and the passenger elevator down. What is his average rate in feet per minute for the entire ride, if the freight elevator travels at the average rate of 3 seconds per foot, while the passenger elevator goes at 3 feet per second?

well they dont tell me anything except the question, a few of my classmates said that you just make up and number

well they dont tell me anything except the question, a few of my classmates said that you just think of a number

thats because i dont understand...

NoName has got it!

Answer 1

Just set up the formulas first.

This is standard R X T = D

Up rate is 3 sec / ft = how many ft/sec? (you should do this)
Down rate is 3 ft / sec
D = 2 floors

Up = R X T = 3 sec/ft X Tu
Down = R X T = 3 ft / sec X Td

So since they didn't give you the actual distance, let's pick one! Let's use 30 ft.

Use the formulas above to solve for time to go up and the time to go down.

Add them together and this will give you the total time.


So now, go back to R X T = D

We now know total time and total distance, so rate is easy!

R = D / T = 60 ft / total time

Hope that helps!

Answer 2

Assume a distance between floors of 60 feet (just to make the maths easy - it doesn't matter how far between floors it actually is the asnswer will be the same).

The freight elevator will travel at 3 seconds per foot so this will take 180 seconds (60 x 3) while the goods lift will travel at 3 seconds per foot and take 20 seconds (60 / 3).

The total journey time will be 200 seconds so the average trip will be 100 seconds (200 seconds / 2 trips). The distance travelled per trip is 60 feet so the average speed in feet is 1.6667 (100 / 60).

Mathematically speaking : if D = distance and S = feet per second the answer can be worked out thus :

((D * SG) + (D / SF)) / 2 = Ave trip speed

since we know the speed each lift travels at we can substitute these into the equation

(3D + 1/3D) / 2

(3 1/3D) / 2

1.6667 feet per second

Answer 3

Intuitively, we believe that we don't have enough information to calculate the actual rate in feet per minute, but that we can express it in terms of the unknown
x= the distance in feet between the floors.

Let's see if our initial intuition is correct, by working through this.

It's not very clearly stated, but it appears the total ride involves starting at one floor, going to the adjacent floor, then returning to the original floor.

Let's call the average rate = R
Total distance = D
Total time = T
R = D / T

D = the total distance = 2X, (X feet there, plus X feet back).

Ok, then what is the total time?
Time of each "leg" of the journey is rate (speed) times distance.
Total time T is simply the sum of the times of the two legs of the journey:

T = ( (3 seconds/foot)* X feet ) + (1 second/3feet) * X feet)
T = 3X + 1/3 X seconds (the feet units cancel!!)
distributive rule says this is same as (3 + 1/3)*X seconds
or (10/3)X seconds
R = 2*X feet / (10/3)*X seconds
we've already seen the feet units cancel; now the X value cancels!!
R = 2 / (10/3) feet / second
R = 2 * (3/10) feet / sec = 6/10 = 3/5 feet/sec

now convert to feet per minute, knowing 60sec/1min = unity.
R = 3/5 feet/sec * (60sec / 1 minute)
= (180/5) feet/minute

R = 36 feet per minute.

Surprise! We have an average rate, and we didn't need to know the distance between floors. The distance and its associated unit (feet) cancelled out of the intermediate equations.

I hope this helps and I'm not getting too tired to think straight.

Glenn

Answer 4

Well to start off, the freight elevator is traveling at 3 sec per foot which is 1/3 feet per sec. Then you take the average of the two elevators to get your average, which will be in feet per seconds. Then you need to convert it into feet per minute, to do that all you have to do is multiply your answer by 60 since 1 minute = 60 seconds. The equations should look like something like this ( # ft / sec) * (60 sec / min) = ( # ft / min). The seconds cancel out and then you have feet per minute. Well thats what I think, hope it helps.

Answer 5

Well, you have to change them to the same unit. So 3 seconds per foot (or to say it more easily, 1 foot for 3 seconds) is the same as 1/3 foot per second. So you average that plus the second thing (3 feet per second).

1/3 + 3 = 3 1/3 and then divide that by 2 to get the average. First change 3 1/3 to an improper fraction to make it easier:

10/3 divided by 2 is the same as 10/3 x 1/2:

10/6 =
5/3 = feet per second. But they want feet per minute. There are 60 seconds in a minute, so:

5/3 ft per sec x 60 sec per min =

5/3 x 60/1 =

300/3 =

100 feet per minute

Answer 6

freight elevator: 3 seconds per foot = 3s/f = 1/3 f/s
passenger elevator: 3 f/s

let x be the distance to travel

time to travel up: = x/(1/3) = 3x
time to travel down = x/3

distance travelled = 2x
average speed = 2x/(3x+x/3) = 6/10 = 3/5 ft/s

Answer 7

ok. firstly, try to convert everything to feet per minute (or FPM).
freight elevator = 3 sec per foot = 1 foot per 3 sec (1minute has how many secs? now's the time to do your own calculation =} )

passenger elevator = 3 feet per sec ( do the same thing as above)

so wat does average rate mean? means u add all the rates together and divide by the total number of rates.

Answer 8

Do they tell you how many feet apart the floors are? Because I don't believe you can average it unless you know the total feet travelled...??

Well, the most help I can be right now unfortunately is to get your rates the same first...instead of thinking of it as 3 sec/ft and 3 ft/sec, think of it as 1/3 ft or 0.33/sec and 3 ft/sec.... hope that helps somewhat... good luck.

Answer 9

change freight elevator speed from sec/feet to feet/sec by dividing
1 / 3 = 0.333... (continued) add 0.333... feet/s to 3 feet/s
0.333... + 3 = 3.333... feet/s now divide 3.333... by 2
3.333... / 2 = 1.666... (continued) or 1.67 (rounded) 1.666... or 1.67 is the average travel rate in feet/s now multiply that by 60 to get the feet/minute which totals out to average travel rate of 100 feet per minute.

Answer 10

The answer is "The piece of sugar-free gum contains 24 calories"