Henry can paint the house in 4 hours, and Claude can paint the house in 3 hours. How long would it take the tw

Question

Henry can paint the house in 4 hours, and Claude can paint the house in 3 hours. How long would it take the two of them to do the job together?

1. 3.5 hours
2. 2 hours
3. 1.75 hours
4. 1.71 hours

Answer 1

The answer is 1.71 hours. Here's how you do it:
In one hour, Henry can do 1/4 of the job, or 3/12. In one hour, Claude can do 1/3, or 4/12. In one hour, they can do 7/12 of the job together. So, they need 1 and 5/7 hours to complete the entire task, which is 1.71 hours

Answer 2

This is a famous problem type. Learn how to solve it, cause you'll see it again and again.

The trick is to express how much of the job each one can do in an hour. Henry can do 1/4 of the job in an hour. Claude can do 1/3 of the job. So together, they can do 1/4 + 1/3 per hour, which is 3/12 + 4/12 = 7/12 of a job per hour. Now, you divide 1 (the number of jobs needing done) by 7/12.

That is 1 * 12/7 = 1 and 5/7 hours.

Divide 7 into 5 to get .71

So it would take 1.71 hours.

You'll see this problem in many forms. One pipe can fill a pool in 6 hours, the other in 3 hours, etc. They all work this way.

Answer 3

Henry can paint the house in 4 hours, and Claude can paint the same house in 3 hours. How long would it take the two of them to do the job together?


If you multiply the speed of house painting (houses/hour) by the number of hours, you get the number of houses, because the hours units cancel out.

Henry and Claude, when painting together, are painting for the same amount of time, let's call that T.

Then the total amount of houses that Henry paints in time T is
T x 1/4 = T/4, because he paints 1 house in 4 hours alone.

The total amount that Claud paints is T x 1/3 = T/3 for the same reason.

So the total amount of houses they paint together is T/4 + T/3. But you know they together paint exactly one house in that time, so:

1 = T/4 + T/3. If you now solve for T,
you will have your time (expressed in hours), LCD = 12,

(12)*(1) = (T/4 + T/3)*(12) Multiply both sides by LCD (12).

12 = 3T + 4T add together

12 = 7T divide both sides by 7

12/7 = T, so

T = 12/7 or 1.714 hours
your answer would be number 4.
1.71 hours

Answer 4

Henry: 4 hours = 1 house => 1 hour = (1/4) house
Claude: 3 hours = 1 house => 1 hour = (1/3) house

Together: 1 hour = (1/4) + (1/3) = 7/12 house

Since 7/12 house = 1 hour,
1 house = 1 x 12 / 7 hours
1 house = 12/7 hours
1 house = 1.714 hours

So the answer is 4) 1.71 hours.

Answer 5

Answer should be 1.71 hours if the 2 painters are machines.

But since we are talking about human, there must be dispute amonge Claude and Henry. Claude will then stop painting when he painted half of the house and let Henry got on with it. And so either:
(1) Henry carries on and finishes his half - then answer = 2 hours
or
(2) Henry stops because Claude has stopped - then answer = unfinished.

Answer 6

Henry paints 1 house/4 hrs, so Henry's speed (call it Sh) is 1/4 or 0.25 house/hr. Claude paints at Sc = 1/3 house/hr.

In time t, (Sh)t + (Sc)t = 1 house

So t = 1 house/(Sh + Sc) = 1/(1/4 + 1/3)

You have to reduce the fractions to a common denominator:

1/4 = 3/12, 1/3 = 4/12

So t = 1/(3/12 + 4/12) = 1/(7/12) = 12/7 = 1.71

Of course, this is only theoretical. In real life the two would divide the work, Claude would finish his in 1.5 hours but it would take Henry 2 hours to finish his half. Remember, there's always more (Sh)t around your house than you expected.

Answer 7

Henry paints 1/4 of the house per hour.
Claude paints 1/3 of the house per hour.

Assume x is the number of hours that it will take for both of them to do it, you can say:
1/4*x+1/3*x=1

So, x=12/7, which is 1.71 hours

Answer 8

So Henry can paint 1/4th house in 1 hr. Claude can do 1/3rd in 1 hr. Between two of them, they can get 7/12 house in one hour. The rest 5/12 can be done in next .71 hrs.

So 4. It wil take 1.71 hours.

Answer 9

Henry = 1/4 and Claude = 1/3
Equation > 1/4 + 1/3 = 1/x hrs.

First: eliminate fractions-multiply the denomiantors by everything...

4(3)(x)(1/4) + 4(3)(x)(1/3) = (4)(3)(x)(1/x)

Sec: cross cancel "like" terms & combine the remaining terms...

(3)(x)(1) + 4(x)(1) = (4)(3)(1)
3x + 4x = 12
7x = 12

Third: solve for "x" by isolating it on one side > divide both sides by 7...

7x/7 = 12/7
x = 12/7 or, 1.71

Answer 10

4. 1,71 hours

Henry can paint the house in 4 hours that mean he makes 25% of the
job in 1 hour (1/4).

Claude can paint the house in 3 hours that mean he makes 33% of the job in 1 hour (1/3).

Together they make 1/4 + 1/3 of the job in 1 hour
1/4 + 1/3 = 7/12

(7/12)*X = 1
X = 0,714....