SOLUTION: Brown can plant his lettuces in an hour and a half.His son could plant them in two and a half hours.How long would it take them if they worked together?

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Question 1195305: Brown can plant his lettuces in an hour and a half.His
son could plant them in two and a half hours.How
long would it take them if they worked together?
Found 3 solutions by ikleyn, math_tutor2020, greenestamps:
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website!
.
Brown can plant his lettuces in an hour and a half.
His son could plant them in two and a half hours.
How long would it take them if they worked together?
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Brown makes = = of the job per hour. It is his rate of work. His son makes = = of the job per hour. It is his rate of work. Their combined rate of work is the sum + = = of the job per hour. Hence, it will take of an hour to complete the job, working together.

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
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    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
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The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

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Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

1 and a half = 1 + 1/2 = 1.5
2 and a half = 2 + 1/2 = 2.5

1.5*2.5 = 3.75

Let's say there are 375 plants of lettuce.
I'm picking this number so that the division results of the next two paragraphs are whole numbers.
The number is derived from moving the decimal point on 3.75 two spots to the right to arrive at 375.

Brown can plant all that lettuce in 1.5 hours if he works alone.
His unit rate is 375/(1.5) = 250 plants per hour.
The unit rate is found by dividing the number of plants over the time needed.
Think of the formula distance = rate*time which rearranges into rate = distance/time.
In this case, "distance" is the amount done, aka the amount planted.

The son can do the same job, when working alone, in 2.5 hours. The son's unit rate is 375/(2.5) = 150 plants per hour.

If the two work together without getting in each other's way, then their combined unit rate is 250+150 = 400 plants per hour.

x = number of hours they work together
400x = amount planted
400x = 375
x = 375/400
x = (15*25)/(16*25)
x = 15/16
x = 0.9375

Answer as a fraction = 15/16 of an hour
Answer as a decimal = 0.9375 of an hour

If you wanted to convert to minutes, then,
0.9375 hrs = 0.9375*60 = 56.25 min
which further breaks down into
56.25 min = 56 min + 15 sec
because 15 seconds is 15/60 = 1/4 = 0.25 of a minute

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Here is a very different way to solve "working together" problems like this.

Consider a convenient common multiple of the two given times for the two workers working alone. For this problem, 15 hours is a nice choice: 1.5*10 = 15; 2.5*6 = 15.

In 15 hours, Brown could do the whole job 15/1.5 = 10 times; in 15 hours his son could do the whole job 15/2.5 = 6 times.
So together in 15 hours the two could do the whole job 10+6 = 16 times.
So to do the single whole job once would take them 15/16 hours.

ANSWER: 15/16 hours