Word Problems Strategy Guide (3) - 5th ed. Chap. 2 Prob. Set

[cliffordlfoster]

In the Word Problems Strategy Guide, question number 8 of the Chapter 2 problem set states the following:

Mary and Nancy can each perform a certain task in m and n hours, respectively. Is m < n?

(1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m.
(2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n.

I understand the answer explanation. However, in proving the sufficiency of statement 1, the strategy guide performs the following operation:
1. (1/m + 1/n)t = 1
2. ((m + n)/mn)t = 1
3. t = (mn)/m + n

I don't understand what operation was performed to get from step 1 to step 2 or why.

[messi10]

Its the process of combining 1/m and 1/n. The reason to combine is that you need the answer in terms or time or variable t i.e. you need t on one side of the equation and everything else on the other. In order to do that, you first need to perform the addition to combine the two fractions.

The process is that of adding fractions together by taking the common denominator. If you are having problems adding variables, try it with real numbers:

e.g. 1/4 + 1/3

Its the same process with variables.

If you struggle with these then just google "adding fractions" and you will find plenty of resources on this including video explanations on youtube

[RonPurewal]

The process is that of adding fractions together by taking the common denominator. If you are having problems adding variables, try it with real numbers:

e.g. 1/4 + 1/3

Its the same process with variables.

If you struggle with these then just google "adding fractions" and you will find plenty of resources on this including video explanations on youtube

this is almost exactly what i was going to write. nice.