Please help me with this 5th grade math problem!?

Question

Here's the problem:
If 6 men take 3 days to dig 8 ditches, then how long would it take for 4 men to dig 10 ditches? Assume that all the ditches are the same size, and take equal amount of time to dig, that all men work at the same steady rate. Solve this problem by using logical thinking and by using the most elementary reasoning you can. Explain clearly.

Please help me in this. If I dont get this problem in time for class tomorrow, I won't get an A in the class!

Answer 1

6 men take 3 days to dig 8 ditches.

So 1 man can dig (8 / (3 x 6)) = 4/9 ditches per day.
Then 4 men can dig 4 x 4/9 = 16/9 ditches per day.
Finally, 10 / (16/9) = x.

x = 45 / 8 = 5 and 5/8 days. Rounded up it's 6 days.

Answer 2

First we assume that all men are able to work at the exact same rate. This means that we can solve a value (I'll call D) of units ditches per man day. This means, how many ditches can one man dig in one day. I'll set up a formula where di = ditches dug, m = men used and da = days taken.

D = di / (m * da)
D = 8 ditches / (6 man * 3 days)
D = 8 ditches / 18 man days
D = 8 / 18 = 4 / 9 ditches per man days

Now we can use the same formula to solve the second half of the problem.

D = di / (m * da)
4 / 9 = 10 / (4 * da)
16 / 90 = 1 / da
da = 90 / 16 = 45 / 8 = 5.625 days = 5.625 * 24 hours = 135 hours

Answer 3

Well I gave it a shot and figured that
3 days to do 8 ditches is 2+(2/3) ditches per day.
6 men to do 2+(2/3) ditches per day
so 1 man does 4/9 of a ditch in one day

working at equal rates, 4 men will do 16/9 ditch per day
you want 10 ditches so you need 5 days and 15 hours.

I hope someone gets the same answer as me.Good Luck with your class.

Answer 4

it takes (6*3)=18 man days to dig 8 ditches
now divide 18 by 8 to find how many man days per ditch:

18/8 = 2.25 man days per ditch

10 ditches will take 10 x 2.25 = 22.5 man days required

since you have 4 men working divide the man days by 4:

22.5/4 =5.625 or 5 5/8 days

Answer 5

The amount of work is often counted in person-years or person-days.

Here, looks like person-days might be useful. One person working 10 days is the same as 10 persons working one day, or 5 persons working two days, etc. All these examples are 10 person-days.

8 ditches require 6 persons * 3 days = 18 person-days.

Then 10 ditches will require (10/8)*18 person days = 22.5 person-days of work.

you have 4 persons on the job so that they will have to work 22.5 / 4 = 5.625 days each.

Answer 6

Okay, I think I may have it.

Take 8 ditches, and divide by 3 days to equal 2.667 ditches per day.

2.667divided by 6 men equal 0.4445 ditches per day EACH.

Then you start using your other numbers...

0.445 times 4 men equal 1.778 ditches per day

10 ditches divided by 1.778 ditches per day equals 5.6 days, which is your answer

I think this is the answer, but let me know if it's wrong.

Answer 7

6 people*3days = 18 people-days to dig 8 ditches
or 9/4 people-days per ditch
for 10 ditches, it will take 22.5 people-days
22.5 people-days/4people = 5.625 days

Answer 8

6men X 3days (24hrs) = 8ditches
so that's 144 man hours = 8ditches
144/8 = hrs per ditch
10 ditches x hrs per ditch / 4 men
hope this helps you