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Is there an easier way to get the answer? I can get the formula. But when I find the root it really takes too much time. How do i solve this in 2 min? Should I back solve by dividing all the answers by 2?
Answer Choice is 12.
For Time and Work problems, If A takes x hrs to do a work and B takes y hours to do a work they combindly do the work in n hrs
Formula is => 1/x+1/y = 1/n
Here Tom takes x hrs to type 20 pages So Jack takes (x+2) hrs to type 20 pages
So Tom takes 5x/4 to type 25 Pages => Jack takes 5(x+2)/4 hrs to type 25 pags
They both completed typing in 3 hrs, accoring to above formula (1/(5x/4)) +(1/(5(x+2)/4)) = 1/3
This leads to an equation 5x^2-14x-24 = 0 Since x cannot be less than zero x =4 x = Time taken by Tom to type 20 pages. So Jack takes 6 hrs to type 20 pages => Jack takes 12 hrs to type 40 pages.
If anybody wants it, here's a pure algebra solution (didn't take very long):
J can do 20 pages in J hours; let's call 20 pages "1 job". So J can do 1/j part of job in 1 hour. T can do 20 pages in T+2 hours; T can do 1/(j - 2) part of job in 1 hour.
Together they can do 1/j + 1/(j - 2) = (2j - 2) / (j^2 - 2j) {common denominator} in 1 hour, so reciprocal: it takes (j^2 - 2j) / (2j - 2) hours to do 1 job or 20 pages.
It must take 5/4 of this to do 25 pages, which is also stated to be 3 hours. So
5*(j^2 - 2j) / 4*(2j - 2) = 3
which means 5j^2 - 10j = 24j - 24, or 5j^2 - 34j + 24 = 0, or (5j - 4)(j - 6) = 0, {no need for quadratic formula} so j must be 6 (can't be 5/4 because then no way to subtract 2 hours for Tom).
If j does 20 pages in 6 hours, must do 40 pages in 12 hours.
This problem was also posted in PS subforum. Below is my solution from there.
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? A. 5 B. 6 C. 8 D. 10 E. 12
Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j-2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour --> \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\) --> \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) --> \(j=6\) --> \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
This problem was also posted in PS subforum. Below is my solution from there.
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? A. 5 B. 6 C. 8 D. 10 E. 12
Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j-2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour --> \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\) --> \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) --> \(j=6\) --> \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
Hellooo ... Can somobody exolain how to solve -5T^2 + 14T + 24 = 0 ? or similar equations? (not the simple ones, they are easily solvable) with quadratic formula? or any shortcut? thanks
this equation is same as 5T^2 - 14T - 24 = 0. now we need to find the value(s) of T for which left hand side of this equation will become '0', i.e., value(s) of T for which this equation will be satisfied. One method which sometimes works is the factorisation method which is basically this:
for a quadratic equation ax^2 + bx + c = 0 we first need to find 2 quantities whose sum is 'bx' and product is 'cax^2' and then we can split the middle term accordingly, eg, in your example equation 5T^2 - 14T - 24 = 0 we need to find 2 quantities whose sum is -14T and whose product is 120T^2. the two such quantities are -20T and 6T. so using these the equation can now be written as:
5T^2 - 14T - 24 = 0 5T^2 - 20T + 6T - 24 = 0 ..... now we can factorise easily as: 5T(T - 4) + 6(T - 4) = 0 which gives us (5T+6)(T-4) = 0 ... now we will put each of the two brackets equal to zero to get two values of T:
5T + 6 = 0 gives us T = -6/5 and T - 4 = 0 gives us T = 4... and these two values are the solution of the equation
Forget all that quadratic equation rubbish, YOU WILL NOT HAVE TO TIME TO DO THIS IN THE EXAM!!!!!
I got the equation, attempted to solve but was already 4mins down or something...
Just sub the answers and get the solution, best way to do it. People don't want to solve it that way on here because it isn't an elegant method, WHO CARES... you get the right answer
This problem was also posted in PS subforum. Below is my solution from there.
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? A. 5 B. 6 C. 8 D. 10 E. 12
Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j-2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour --> \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\) --> \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) --> \(j=6\) --> \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
Answer: E.
Hope it helps.
Great explanation, but I used (20/j)+(20/j+2) instead of (20/j)+(20/j-2) and it of course does not work... Why do you subtract 2 from j instead of adding it? Question says "jack takes two hours longer" so it seems natural to add.
This problem was also posted in PS subforum. Below is my solution from there.
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? A. 5 B. 6 C. 8 D. 10 E. 12
Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j-2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour --> \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\) --> \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) --> \(j=6\) --> \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
Answer: E.
Hope it helps.
Great explanation, but I used (20/j)+(20/j+2) instead of (20/j)+(20/j-2) and it of course does not work... Why do you subtract 2 from j instead of adding it? Question says "jack takes two hours longer" so it seems natural to add.
Posted from my mobile device
It takes Jack 2 more hours than Tom to do the job --> J is greater than T by 2 --> J = T + 2 --> T = J - 2.
It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?
Sol: Combined rate of Jack and Tom is 25 pages in 3 hours so 8.33 pages per hour.
Let's take option C So jack takes 8 hours to type 40 pages or 5 pages per hour. For 20 pages Jack will take 4 hours and Tom will take 2 hours to type 20 pages So, (Jack's rate+Tom's rate)*3= 25 pages but Jack's rate=5 and Tom's rate= 10 so not possible
Option A, B and C can be easily ruled out.
Option D, So Jack's rate: 4 pags per hour So 5 hours to type 20 pages and Tom's rate will 3 hours for 20 pages (Combined rate = 4+6.66)*3 is not equal to 25.
Hence Ans E _________________
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