One person can dig a hole in 50min, another person takes 40min, how long if they work together?

Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!

Popular Math Courses:

Math Foundations

Math Skills Rebuilder Course:

Pre-Algebra

Algebra

Geometry

Algebra 2

Pre-Calculus

• MIDDLE & HIGH SCHOOL MATH
• HOMESCHOOL MATH
• COLLEGE MATH
• TEST PREP MATH
• TEACHER CERTIFICATION TEST MATH

[dazartingstall]

In real life, ten minutes after they start, Dan accuses John of being a slacker and John counters with accusations that Dan's a company toady. After the ensuing fisticuffs, they both get sacked. The time wasted leads to the firm losing the contract, and a rival outfit sends Pete, who does the job in 30 seconds with a JCB.

[larryo]

My logic, let’s say both can dig a hole in 50 min so together they can dig a hole in 25 min, then let’s say both can dig a hole in 40 minutes so together they can dig a hole in 20 minutes. However since one can dig at 50 and the other at 40 the answer has to be between 20 to 25 minutes and the only choice therefore is 22.2 minutes.

[fred]

22.2. Add the rates, then take the reciprocal

[dazartingstall]

Dan = 1/50 holes per minute
John = 1/40 hpm
1/50 + 1/40 = 9/200
1 ÷ 9/200 = 200/9
200/9 = 22.2 minutes

[jamesmoeller]

Two guys at 40, 20 min
Two guys at 50, 25 min
Probably between these two?
Average = 22.5?

[armchairtin-kicker]

Given r * t = w, then r = w/t (or unit of work for an allotted time)

Dan completes 1/50 of the work in one minute and Jon completes 1/40 of the work in one minute.


(1/50 + 1/40)*t = 1
(1/(2*5^2) + 1/(2^3*5))*t = 1
((2^2 +5)/(2^3*5^2))*t = 1
(9/200)*t = 1
t = 200/9
t=22.2

Therefore, the time working together is 22.2 minutes, so the answer is "c."

[mauriziograndi]

Time vs Work done.
Dan works at the speed of 1.2 unit per minute. (60/50)
Jon speed is 1.5 unit per minute. (60/40)
Together their speed is 2.7 unit per minute.
60/2.7 = 22.2 minutes

[Set_Get]

answer a] is arithmatic mean. answer c] is called Harmonic mean. it goes on to show why harmonic mean is important and useful, particularly in physics.

[It.s-just-me]

2 hrs. and 45 minutes...
Because they're in each other's way now.

(22½ minutes if it's big enough for them to both work comfortably)

[gavindeane]

In 200 minutes Dan can dig 4 holes and Jon can dig 5, so 9 holes in total.

Therefore digging one hole takes them 200/9 minutes. That's 22.2 recurring minutes, so none of the answers is correct, but answer c is closest.

[tonysid]

12 hours. Dan and John both joined the union and found enough reasons to put the job off until the end of the week. As the company requires that the job be completed before the next Monday, Dan and John had to do the work on overtime. They worked 8 hours on Saturday at time and a half. Then they worked 4 hours on Sunday at double time.
This provided each with 20 hours extra pay to do what either could have done in less than 1 hour alone on regular time. 😊

[johnmarchington]

I think the answer is the reciprocal of the sum of the reciprocals; i.e. 1/c = 1/50 + 1/40, or 4/200 +5/200. So 1/c = 9/200, so c = 200/9, or 22.2. So my answer is (c).

[shimxininahi]

I always wanted to know this. You could determine how fast you want the job done. Now we can figure out what size excavator bucket and project completion time. This could also estimate rental usage. Cut the labor and enjoy more cold ones. Thanks!

[pegaldiss]

It's at 8:37 minutes and still waiting for the explanation. Considering bailing - reminds me so much of school, lost interest while waiting for it to get somewhere....

[joeschmo]

(40x50)/(40+50) = 2000/90 = 200/9 = a little more than 20 (200/10), so 22.2min.

(Same formula as the parallel-resistors formula.)

[rick_.]

Simple solution: each digs half of the hole. Average of 40/2 and 50/2 is 22.5.

[robertthompson]

The theoretical mathematical solution will be completely different to a real time situation due to various logistical factors such as how many shovels can you fit in the hole at the same time or if a machine is being used then only one operator is required. Or if the workers start chatting to each other.

[Lucinda-zrsu]

Thanx for all of the comments. Very entertaining. Its good for someone like me to be able to chuckle while figuring and computing. Math was never my strong suit.

[GPRaitsakas]

Using the simple product divided by sum formula gives the answer of 22, 2 in one easy step.

[andrewharris]

It’s just a matter of ratios, not necessarily algebra. They work in ratio 4:5. Together 4:(4+5)or5:(4+5), depending on from whose POV you’re considering the question. Either way you get 200/9 minutes.