Question

A secretary and a trainee are processing a pile of 124 forms. The secretary processes 15 forms per hour while the trainee processes 7 forms per hour. If the trainee begins working at 9:00 am. and the secretary starts working after 2 hours, then at what time will they finish the pile of forms?

Answer 1

Let the number of hours the trainee works = $t$ hours.

According to the question, the secretary starts working after two hours. Since they finish the pile of forms together, the secretary works 2 hours less than the trainee, i.e., $(t-2)$ hours.

In one hour, the trainee processes 7 forms.
$\therefore$ In $t$ hours, $7t$ forms will be processed by the trainee.

In one hour, the secretary processes 15 forms.
$\therefore$ In (t-2) hours, 15(t-2) forms will be processed by the secretary.

Now, since all the forms are processed, their total is equal to the total number of forms, i.e., 124.
$\therefore 7t+15(t-2)=124$
$\Rightarrow 22t=154$
$\Rightarrow t=7$ hours.
7 hours from 9:00 am is 4:00 pm.

$\therefore$ They took 7 hours to process the pile of 124 forms.