rates

manelgirona wrote:If 50 apprentices can finish a job in 4 hours and 30 skilled workers can finish the same job in 4 1/2 hours, how much of the job should be completed by 10 apprentices and 15 skilled workers in one hour?
a) 1/9
b) 29/180
c) 26/143
d) 1/5
e) 180/29
The answer is B. How would you solve it

My strategy is to determine what can be accomplished bt in worker in 1 unit of time (i.e., 1 hour or 1 day or 1 minute etc) and then go from there.

50 apprentices can finish a job in 4 hours
So, in 1 hour, 50 apprentices will complete 1/4 of the job
So, in 1 hour, 1 apprentice will complete 1/200 of the job (1/4 x 1/50 = 1/200)
So, in 1 hour, 10 apprentices will complete 1/20 of the job (1/200 x 10 = 1/20)


30 skilled workers can finish the same job in 4.5 hours
So, in 1 hour, 30 skilled workers will complete 1/4.5 of the job
So, in 1 hour, 1 skilled worker will complete 1/200 of the job (1/4.5 x 1/30 = 1/135)
So, in 1 hour, 15 skilled workers will complete 1/9 of the job (1/135 x 15 = 1/9)

Working together for 1 hour, 10 apprentices and 15 skilled workers will complete 1/20 + 1/9 of the job
1/20 + 1/9 = 29/180 (B)