NEED FORMULA

SMS1991

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Feb 8, 2006
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1 MAN SHOVELS DRIVEWAY IN 3 HRS
1 MAN SHOVELS IT IN 2 HRS
HOW LONG WILL IT TAKE TO SHOVEL DRIVEWAY WORKING TOGETHER?
 
steven stainbrook said:
1 MAN SHOVELS DRIVEWAY IN 3 HRS
1 MAN SHOVELS IT IN 2 HRS
HOW LONG WILL IT TAKE TO SHOVEL DRIVEWAY WORKING TOGETHER?

There is no formula, but you can set it up if you think about it.

The first man can do the job in 3 hours, so he does 1/3 of the job per hour.

The second man can do it in 2 hours, so he does 1/2 job per hour.

They work x hours when they're working together.

Their combined work will do the whole job, so (1/3)x + (1/2)x = 1 job.

multiplying, you get x/3 + x/2 = 1

Get a common denominator and add, then finish solving.
 
Kindly please turn off "CAPS LOCK", so you're not SHOUTING. Thank you.

"One man shovels a drive in three hours. Another shovels it in two hours. How long would they take to shovel the drive together?"

Convert the times into rates:

. . .hours to complete job:
. . . . .slow guy: 3
. . . . .fast guy: 2
. . . . .together: t

. . .completed per hour:
. . . . .slow guy: 1/3
. . . . .fast guy: ??
. . . . .together: ??

Complete the table.

Add how much they each do in an hour, and set equal to what they do together in an hour. Solve for the value of "t".

Eliz.
 
steven stainbrook said:
1 MAN SHOVELS DRIVEWAY IN 3 HRS
1 MAN SHOVELS IT IN 2 HRS
HOW LONG WILL IT TAKE TO SHOVEL DRIVEWAY WORKING TOGETHER?
I'm struggling with this one just a bit. It isn't quite clear to me that there are two men. The answer may be "2 hrs" since he managed a shorter time on the second attempt.
 
steven stainbrook said:
1 MAN SHOVELS DRIVEWAY IN 3 HRS
1 MAN SHOVELS IT IN 2 HRS
HOW LONG WILL IT TAKE TO SHOVEL DRIVEWAY WORKING TOGETHER?

The secret to solving these types of problems is to find the fractional part of the task done in one unit of time (e.g. weeks, days, hours, minutes, etc.). Add the fractional parts and you get the fractional part of the task they do together in one unit of time (the unknown in your example).

Let x = number of hours to shovel

Thus

1/3 + 1/2 = 1/x

Multiply the whole thing by the LCD (6x) to clear fractions and you get

2x + 3x = 6

5x = 6

Isolate x

x = 6/5
 
There is a general expression for solving problems of this type which the folowing example will illustrate.

If it takes me 2 hours to paint a room and you 3 hours, ow long will it take to paint it together? >>

Method 1:

1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.
 
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