This question has to do with equations & inequalities: 
Fanny can type 150 words in 3 minutes. 
Therefore Fanny's typing rate is 150 word per 3 minutes, or  or
 or 
 or 50
 or 50 
 
Gerard can type 160 words in 4 minutes. 
Therefore Gerard's typing rate is 160 word per 4 minutes, or  or
 or 
 or 40
 or 40 
 
how long would it take Fanny & Gerard, working at the same time, to type a 1,800-word report.
Let the answer be x minutes.
Their combined rate, when working at the same time is 50+40 = 90 .
RATE times TIME = PRODUCTION
            90x = 1800
              x = 20 minutes.
Checking: at 50 words per minute, in 20 minutes Fanny types 50*20 or 1000
words.  And in 20 minutes Gerard types 40*20 or 800 words, and sure enough
together they type 1000+800 or 1800 words in 20 minutes.
Edwin
.
RATE times TIME = PRODUCTION
            90x = 1800
              x = 20 minutes.
Checking: at 50 words per minute, in 20 minutes Fanny types 50*20 or 1000
words.  And in 20 minutes Gerard types 40*20 or 800 words, and sure enough
together they type 1000+800 or 1800 words in 20 minutes.
Edwin