Solve Ratio Word Problem: A & B in 30 & 40 Days

[alijan kk]

Homework Statement

A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

Homework Equations

The Attempt at a Solution

I just imagined walls and paiting work and try to assign them

and i found that it tooks 55 days working together ?
but i don't know how can i approach this kind of problems

and in my notes the ans is 17+1/7 days

 

[Mark44]

Homework Statement

A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?

Homework Equations

The Attempt at a Solution

I just imagined walls and paiting work and try to assign them

"painting" ?

and i found that it tooks 55 days working together ?

Does this make sense? B working alone can do the work in 40 days. Why would it take 15 days longer if both of them are working

but i don't know how can i approach this kind of problems

and in my notes the ans is 17+1/7 days

Look at the problem in terms of what each person can do in one day. A can do 1/30 of the job per day, and B can do 1/40 of the job. How much can they do together in a day?

 

[alijan kk]

"painting" ?
Does this make sense? B working alone can do the work in 40 days. Why would it take 15 days longer if both of them are working

Look at the problem in terms of what each person can do in one day. A can do 1/30 of the job per day, and B can do 1/40 of the job. How much can they do together in a day?

7/120 work a day together ?

 

[Chestermiller]

This is basically a rate-time-distane problem. If it takes A 30 days to do a job working alone, what is his rate of doing work, in jobs/day. If it takes B 40 days, what is his rate of doing work, in jobs/day. How many jobs does A do in t days? How many jobs does B do in t days? How many jobs do A and B do together in t days?

 

[alijan kk]

This is basically a rate-time-distane problem. If it takes A 30 days to do a job working alone, what is his rate of doing work, in jobs/day. If it takes B 40 days, what is his rate of doing work, in jobs/day. How many jobs does A do in t days? How many jobs does B do in t days? How many jobs do A and B do together in t days?

A does 1/30 job a day and b does 1/40 job a day,,,,, should i sum up the 1/30 and 1/40 to get the joint working job per day ration ?

 

[Chestermiller]

A does 1/30 job a day and b does 1/40 job a day,,,,, should i sum up the 1/30 and 1/40 to get the joint working job per day ration ?

Please answer my other questions. You're on the right track.

 

[alijan kk]

Please answer my other questions. You're on the right track.

t/30 A and t/40 B

wow, i just got the answer,, thankyou !

 

[Mark44]

A does 1/30 job a day and b does 1/40 job a day,,,,, should i sum up the 1/30 and 1/40 to get the joint working job per day ration ?

Let t = number of hours for A and B working together to finish the job.
Then your equation is $\frac t {30} + \frac t{40} = 1$
Here 1 represents the whole job.
From the above, $\frac {4t}{120} + \frac{3t}{120} = 1$ or $7t = 120$
The published answers follows immediately.