A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how man

Question

A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days, A alone can complete the work

Answer 1

Let A be the number of days to complete the job working alone.
Let B be the number of days to complete the job working alone.

Each day A, does 1/A of the work and B does 1/B of the work. In a day, working together they do 1/7 of the work, so:
1/A + 1/B = 1/7

Also: B = 2A (he takes twice as long as A). Substitute in for B:
1/A + 1/(2A) = 1/7

Get a common denominator of 2A:
2/2A + 1/2A = 1/7

Add:
3/2A = 1/7

Cross multiply:
2A = 21

Divide both sides by 2:
A = 10½ days working alone

Note: don't forget to double check your answer. It should take longer for A working alone compared to working together. If you get a smaller answer, you've made a mistake... (like I did the first time I tried this.)

Answer 2

First you need to define some parameters to solve the problem.

Let's call the amount of work 'units'. Let's make the total number of 'units' to complete a multiple of 7 to make the math easier. I chose 42. Thus, if there are 42 units to complete in 7 days, that means the rate that A&B worked together is 6 units/day.

Since together they completed 6 units/day and A is twice as efficient as B, that means that A complete 4 units/day and B completed 2 units/day.

Now you can solve the problem for A alone.

Completed units = rate*time

42 units = (4 units/day)*time,

Therefore, the time it takes for A to complete the project is 10.5 days

Hope this helps

Answer 3

You have to use rates. A + B = (1 job) / (7 days), or 1/7 job/day. At the same time, A = 2B, because A works at twice the rate of B. You can therefore write A + B = 2B + B = 3B = 1/7, so B = 1/21 job/day. A = 2B = 2/21 job/day, and so A requires 21 days to complete the job twice over, or 10.5 days to complete the individual job.

Answer 4

A&B can complete the work in 7days
Now A can be regarded as =2B
3B can do in 7days
B alone can do in 21 days
2B can do in 10.5 days
or A can do the work in 10.5 days

Answer 5

A=2B
A+B=1/7 days^1
3B=1/7
B=1/21
A=2B=2/21 so
B working alone can do the job in 21/2=10.5 days

Answer 6

assuming the number of days for A to complete work = x; B = y;
1st sentence: x = 2y-------(1)
2nd sentence: x + y = 7---(2)
(1) -> (2)
3y = 7
y= 7/3
From (1);
2*(7/3) = x
Thus, x = 14/3 = 4 and 2/3

Answer 7

rate * time = quantity of work

A = 2B
B = A/2

(A + B ) * 7 = 1
(A + A/2) * 7 = 1
1.5 * 7 * A = 1
A = 1/10.5

A * T = 1
T / 10.5 = 1
T = 10.5 Will take A 10.5 days