Question

Sergei can reorganize the library in 5 hours. His sister Irina can do the job in 10 hours. How long would it take for the two of them to do the job together?

Answer 1

3 1/3 hours

Explanation:

Let the total work done be x

For Sergei

In 5 hours, amount of work done by Sergei = x

in 1 hour ,amount of work done by Sergei = x/5

Similarly for Irina

In 10 hours, amount of work done by Irina = x

in 1 hour ,amount of work done by Irina = x/10

In 1 hour , work done by both of them together = work done by Sergei in 1 hour + work done by Irina in 1 hour = x/10 + x/5 = (x + 2x)/10 = 3x/10

Thus,

we can say that

time taken to do 3x/10 work by both of them together = 1 hour

since the total work is x , to find time taken to do total work together

we divide both side of equation with 3/10

time taken to do 3x/10/ (3/10) work by both of them together = 1/(3/10) hour

time taken to do x work by both of them together = 10/3 hours = 3 1/3 hours.