Sam can plow a field by himself in 14 hours. John can plow the same field in 8 hours.?

Question

How long would it take them, working together to plow that field?

Answer 1

a lot less time

Answer 2

Let x be the number of hours needed for both of them working together to plow one field.

In x hours Sam can plow x/14 of a field.
In x hours John can plow x/8 of a field.

Together they can plow:

x(1/14 + 1/8) = 1 field
x = 1/(1/14 + 1/8) = 1/[(4 + 7)/56] = 1/(11/56) = 56/11 hours

So the answer is 56/11 hours or 5 1/11 hours.

Answer 3

Every hour, Sam can blow 1/14 from a field while John can blow 1/8. So for them to finish the whole field together while each works on his own rate :
(1/14)*x + (1/8) * x = 1
Where:
X=Number of hours they both work (this should be the same since they will start and finish together).
1/14=The rate at which Sam is working
1/8=The rate at which John is working
1: this is equivalent to saying that the whole work is done, which is 14/14 for Sam and 8/8 for John.
Solving the equation:
x/14 + x/8 = 1
Multiply both sides By 14*8 (To make it easier to calculate)
8X + 14 X = 14*8 = 112
22X = 112
X = 5.090909 Hours ≈ 5.091 Hours

From this, we can find the percentages each one worked:
Sam: (1/14)*5.091= 0.3636363 ≈ 36.4%
John (1/8)*5.091= 0.63636363 ≈ 63.6%

Answer 4

in one hour sam plows 1/14 a field. in one hour john plows 1/8 a field so:
[x/14 + x/8 = 1] (* 56)
4X + 7X = 56
11X = 56
X=56/11 OR 5 1/11 hours

Answer 5

First let's determine the part of field can one man plough in 1 hour If they work 56 days 6 hours a day that means that they work 336 hours to plough the field So that means that 30 men in one hour can plough 1/336 of the field Furthermore we get that one man in one hour can plough 1/(336 * 30) of the field now if we have 12 men working they can plough 12/(336 * 30) of the field equals 1/(28 * 30) so if they work 8 hours a day that means that 12 men can plough 8/(28 * 30) of the field in a day equals 1/105 of the field So to plough the whole field 12 men working 8 hours a day need 105 days

Answer 6

Every hour, Sam plows one fourteenth (1/14) and John plows one eighth (1/8) of the field. So, if 1 field is plowed by both:

1 field = [(Sam's acomplishment in one hour) + (John's acomplishment in one hour)] * (total number of hours)

So... using our numbers:

1 = [(1/14) + (1/8)] * x

And solving for x, we get 1/[(1/14)+(1/8)] or roughly 5.09 hours.

Answer 7

Sam = 14hr.
John = 8hr.

If John work alone it would take 8hr. to plow the field.
If Sam works with John then straight away it will take less then 8hr.

The hourly rate to plow the field area (A) by each man:
Sam: 1/14 = 0∙071 428 571 of A.
John: 1/8 = 0∙125 of A

Hourly rate combined = Sam's time + John's time.
Hourly rate combined = 0∙071 428 571 + 0∙125
Hourly rate combined = 0∙196 428 571 of A/hr.

The full area is the full unit:
1/ 0∙196 428 571 = 5∙090 909 091...hr.

5∙090 909 091...hr. = 5hr. + (0∙090 909 091...x 60) min.
5∙090 909 091...hr. = 5hr. + 5∙45454545... min.
5∙090 909 091...hr. = 5hr. 5min. + (0∙45454545...x 60) sec.
5∙090 909 091...hr. = 5hr. 5min. + (0∙45454545...x 60) sec.
5∙090 909 091...hr. = 5hr. 5min. + 27∙272727... sec.
5∙090 909 091...hr. ≈ 5hr. 5min. 27∙3 sec.

To check answer:
The portion of the field Sam plows:
0∙071 428 571 * 5∙090 909 091...= 0∙36363636...of A.
The portion of the field John plows:
0∙125 * 5∙090 909 091...= 0∙63636363... of A.

Total area plowed in 5∙090 909 091...hr :
Sams' portion + Johns' portion =
0∙36363636... + 0∙63636363... = 1 (ie. 100% - answer confirmed).

Time taken is: 5hr. 5min. 27∙3 sec.

Answer 8

Sam can finish 1/14 of the job in one hour ....
And John can do 1/8 of the work in one hour ...

Together they can finish 1/14 + 1/8 i.e. 11/56 portion of the work..

So, they can finish the work together in 56/11 i.e. 5 hours 5.45 min.

Answer 9

11 hours

Answer 10

9.5 hours if sam did 25% and john did 75%

Answer 11

I agree with almightyfredder