P can do a piece of work in x days and Q can do the same work 3x days. To finish the work together they take 12 days. What is the value of x?
Question
P can do a piece of work in x days and Q can do the same work in 3x days. To finish the work together they take 12 days. What is the value of x?
Solution
Sure, let's solve this step by step.
Step 1: Understand the problem P can do a piece of work in x days and Q can do the same work in 3x days. If they work together, they can finish the work in 12 days. We need to find the value of x.
Step 2: Set up the equations The rate of work done by P is 1/x (work/day) and the rate of work done by Q is 1/3x (work/day). When they work together, their combined rate is 1/12 (work/day).
Step 3: Write the equation The combined rate of work is the sum of their individual rates, so we can write the equation as: 1/x + 1/3x = 1/12
Step 4: Solve the equation To make it easier to solve, we can multiply all terms by 12x to get rid of the fractions: 12 + 4 = x So, x = 16 days.
Therefore, P can do the work in 16 days and Q can do the same work in 48 days.
Similar Questions
A and B together can do a piece of work in 8 days, but A alone can do it in 12 days. How manydays would B alone take to do the same work?
X can do a piece of work in 8 days, Y can do it in 10 days and Z can do it in 20 days. In how many days can X, Y and Z together complete the work?
Abhi and Bhanu can do a piece of work in 6 and 12 days, respectively. In how many days the work can be completed if Abhi and Bhanu work together?
.A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A does a work in 12 days and B does the same work in 18 days.In how many days they together will do the same work?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.