Question 1-

WW+JJ+AA=WJA . Solve for W, J, and A. The values must be positive integers and different from each other.

Question 2

There are two researchers who need to build a research report. Together, the two researchers can create a report in four days. One researcher can build the report by herself in six days. How long would it take the other researcher to build the report by himself, assuming all speeds and lengths of reports are consistent?

#just added
Question 3

There is a desert that is growing due to climate change. Every year, the desert doubles in size. If it takes 48 years for the desert to cover the entire country, how long would it take for the desert to cover half of the country?

Thanks and God bless.

dauddy97:
Question 1-

WW+JJ+AA=WJA . Solve for W, J, and A. The values must be positive integers and different from each other.

Question 2

There are two researchers who need to build a research report. Together, the two researchers can create a report in four days. One researcher can build the report by herself in six days. How long would it take the other researcher to build the report by himself, assuming all speeds and lengths of reports are consistent?


Thanks and God bless.

Question 1:
A two digit number is basically 10*Tens Digit + Unit Digit, therefore
WW = 10W + W = 11W
doing the same for others
WW + JJ + AA = 11W + 11J + 11A
A three digit number is 100*hundreds digit + 10* tens digit + unit digit
Therefore
WJA = 100W + 10J + A
finally
11W + 11J + 11A = 100W + 10J + A
moving like terms
10A + J = 89W
Keeping in mind that 1 <= W,J,A <=9
Setting W as 1 we get A as 8 and J as 9
W=1
J=9
A=8

Question 2
Combined rate = 4 days
R1 = 6days
R2 = x days
1/(1/x + 1/6) = 4
1/x = 1/4 - 1/6 = 1/12
X = Researcher 2 = 12 days

user4321:

Question 1:
A two digit number is basically 10*Tens Digit + Unit Digit, therefore
WW = 10W + W = 11W
doing the same for others
WW + JJ + AA = 11W + 11J + 11A
A three digit number is 100*hundreds digit + 10* tens digit + unit digit
Therefore
WJA = 100W + 10J + A
finally
11W + 11J + 11A = 100W + 10J + A
moving like terms
10A + J = 89W
Keeping in mind that 1 <= W,J,A <=9
Setting W as 1 we get A as 8 and J as 9
W=1
J=9
A=8

Question 2
Combined rate = 4 days
R1 = 6days
R2 = x days
1/(1/x + 1/6) = 4
1/x = 1/4 - 1/6 = 1/12
X = Researcher 2 = 12 days

Thanks, the second solution. It will take Research2 12 days to build a report that toke research1 6days.



Another Question-
There is a desert that is growing due to climate change. Every year, the desert doubles in size. If it takes 48 years for the desert to cover the entire country, how long would it take for the desert to cover half of the country?

dauddy97:
Thanks, the second solution. It will take Research2 12 days to build a report that toke research1 6days.



Another Question-
There is a desert that is growing due to climate change. Every year, the desert doubles in size. If it takes 48 years for the desert to cover the entire country, how long would it take for the desert to cover half of the country?

47 years

user4321:

47 years

Thanks so much. you are such a wonderful genius. can u pls explain how u got the 47year. Thought, it's very correct. I just want to know the workings.

dauddy97:
Thanks so much. you are such a wonderful genius. can u pls explain how u got the 47year. Thought, it's very correct. I just want to know the workings.

If the desert doubles in size then the size at any point 2ⁿ * X , where X is the starting area of the desert. The total area can be given as A.
Therefore 2⁴⁸ = A
Half of A = A/2 = (2⁴⁸)/2 =
(2^48-1) = 2⁴⁷
Therefore n' = 47 years

Don't reason too far...
Calm urself and say to urself *this is very simple*
Since for evry 1 year increment,the size double...
Meaning that for every 1 year decrement the size half.
The latter applies here..
From the whole desert back to half the desert it takes just a year decrement.
(48-1)
47yrs...
The above is called analytical solution.
Tho..you can use different numerical approaches

..

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Harbidexy5:
Sorry for the blurred cam

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