Question

In \[30\] minutes, Jenny can type $1200$ words. How many minutes will she take, if she types a $3000$ word essay?

Answer 1

Hint:In this problem, we have given that Jenny can type $1200$ words in $30$ minutes. These types of questions can be solved by work and time relationship. The work done by Jenny is $1200$ words and time taken is $30$ minutes and another work done by Jenny is $3000$ words and time taken to do that work needs to be found.

Formula used:
$\dfrac{w}{t} = \dfrac{W}{T}$
Where, w is the first work done by Jenny and t be the time taken to complete that work and W is the second work done by Jenny and T be the time taken to complete the second work.

Complete step by step answer:
We can easily solve this problem by using the work time relationship,
$\dfrac{w}{t} = \dfrac{W}{T}$
Where, w is the first work done by Jenny and t be the time taken to complete that work and W is the second work done by Jenny and T be the time taken to complete the second work. Let w be $1200$, as the Jenny type $1200$ words and the time taken to complete it is $30$ minutes, which means $t = 30$ and W be $3000$, as the Jenny type $3000$ word essay and we have to find the value of T. Now, substitute the values into the formula,
$\dfrac{{1200}}{{30}} = \dfrac{{3000}}{T} \\
\Rightarrow 40 = \dfrac{{3000}}{T} \\
\Rightarrow 40T = 3000 \\
\Rightarrow T = \dfrac{{3000}}{{40}} \\
\therefore T = 75 \\ $
Hence, the time taken to type the $3000$ word essay is $75$ minutes, or we can say $1hr15\min $.

Note: The time taken to complete the first work is given in minutes, so, if we apply the time value in minutes then the time we get for the second work is also in minutes and we can also change it in the form of seconds, hours etc. but if both the time is given and the form of both is different then we have to change the form of one time according to the other.