How does one do a work problem like this?

Question

Though I do want to know how to do this problem in particular, I also want to know how to do problems like it.

"Susan can do the job in 90 minutes. Together, she and Harry did the job in 40 minutes. How long would it take Harry to do the job alone?"

Answer 1

Harry can do the job alone in 72 minutes.

Susan can do job in 90 min.
so she can do 1/90 of the job per min.
Harry can do the job in x min.
so he can do 1/x of the job per min.

Together, they do 1/90 + 1/x of the job per min.
So 40minutes * (1/90 + 1/x) job/minute = 1 job

40(1/90 + 1/x) = 1
40[(x+90)/90x] = 1
40(x+90) = 90x
40x + 3600 = 90x
3600 = 50x
x = 72 minutes

For questions like this in general, convert the time it takes each individual to do the whole job into the fraction of the job per unit time that they each work. When they work together, these rates at which they work can be added together. This sum, when multiplied by the time equals 1 (the whole job).

Answer 2

In 360 minutes, working alone, Susan can do the job 360 / 90 = 4 times.

In 360 minutes, Susan and Harry together can do the job 360 /40 = 9 times, and since 4 of these jobs "belong to" Susan, the other 5 jobs must "belong to" Harry.

This means that, in 360 minutes, working alone, Harry is capable of doing the job 5 times. Thus, alone, he can do the job once in 360 / 5 = 72 minutes.

I chose 360 minutes because 360 is the smallest common multiple of 40 and 90. I like to approach these problems this way because I can see (in my mind) how the work is really divided up and the solution can usually be found using just whole numbers all the way through.

Answer 3

total time taken by susan= 90 mins
hence in 1 minute, susan completes 1/90 th of the job.
let harry take x minutes to do the entire job alone.
then in 1 minute harry does 1/x of the job.
together they take 40 minutes. hence :
40(1/90 + 1\x) = 1
40( 90 + x)= 90x
3600 +40x = 90x
hence x= 72 minutes.

therefore harry takes 72 minutes to do the job alone.

Answer 4

Fraction of the job Susan can do in a minute is - 1/90
Fraction of the job S & T can do in a minute is - 1/40
Fraction of the job T alone can do in a minute is - 1/40 - 1/90
- do - (simplify) - 1/72
Therefore T can complete the job in 72 minutes.
U can resolve any problem of this nature in the same way.

Answer 5

suppose it takes X minutes for Harry to complete this job alone
then we can get :in the 40 mintues,
since Susan can finish this job in 90 minutes,so her rate is 1/90,therefore ,in the 40 minutes,Susan finished 40*1/90=4/9 of the whole job
the rest job is of course 1-4/9=5/9
remember,Harry finished the rest job in 40 minutes,so Harry' rate should be : 5/9 /40=1/72
in this case ,it takes Harry 72 minutes to complete this job

Answer 6

A basic rate problem, but there are different variants, so don't expect this approach to necessarily solve other problems.

Susan's rate R_s =1 job/90 minutes. Harry's is unknown, but we'll call it R_h.

So, (R_s + R_h)*40 min = 1 job, carrying the units ensures you're calculating meaningful things. Solve for R_h.

By inspection, since it takes 40 minutes, which is less than 1/2 of the time required for Susan to do the job, Harry's rate must be higher, i.e., he can do 1 job in less than 90 minutes.

Answer 7

80 minutes .

Answer 8

Honestly I'm not positive but i would probably assume that the time it takes for both of them to do it would be something like half of the average of both of their times.
S=90
H=x
(S+H)/4=40
90+x=160
x=70
Hope this helps