If Rooney can type a document for 30 minutes and John can type the same document for 40 minutes. If Rooney and John start typing the same document at 1st January; 10:00am. At what date and time will they first finish at the same time.
I actually got the answer but I used a crude method of having to write for both of em. I was wondering if there was a better way to solve the problem using algebra or any other method.
At first I misunderstood this problem thinking it was asking how long it will take them to type the document if they work together- each taking a different page perhaps. But that's not what it's asking. It is asking, rather, if they both type the document repeatedly, how long will it be until they both finish at the same time.
The "least common multiple" of 30 and 40 is 4(3)(10)= 120. 120= 4(30) so, in 120 minutes, Rooney will have typed the document four times. 120= 3(40) so, in 120 minutes, John will have typed the document three times.
Yes, 120 minutes= 2 hours after they started at 10:00 is 12:00 and that will be when they both finish a copy of the document at the same time. If you got something else by your "crude method" then your "crude method" is wrong.
Here is what I would consider a "crude" method: Rooney will complete his first copy at 10:00+ 30 minutes= 10:30, John, at 10:00+ 40 minutes= 10:40, not the same time. Rooney will complete his second copy at 10:30+ 30 minutes= 11:00, John at 10:40+ 40 minutes= 11:20, not the same time. Rooney will complete his third copy at 11:00+ 30 minutes= 11:30, John at 11:20+ 40 minutes= 12:00. Rooney will complete his fourth copy at 11:30+ 30 minutes= 12:00, the same time John complete his third copy.
What I actually did was draw a table, with Column Header Rooney, John.
Something like
Rooney | John
10am Jan 1 | 10am Jan 1
10:30 am Jan 1 | 10:40 am Jan 1
But yes, the LCM method should work. Meaning that at 12:00 am they both Jan 1. They both should finish at the same time. Thanks you two.