Question

one member of a gardening team can landscape a new lawn in 36 hour. The other member of the team can do the job in 45 hours. How long would it take to landscape a lawn if both Gardner's worked together

Answer 1

one member of a gardening team can landscape a new lawn in 36 hour. The other member of the team can do the job in 45 hours. How long would it take to

Answer 2

20 hrs

Explanation:

Given:-

- Time taken by gardner 1 alone, t1 = 36 hr

- Time taken by gardner 2 alone, t2 = 45 hr

Find:-

How long would it take to landscape a lawn if both Gardner's worked together

Solution:-

- We need to see that the time taken (t) to landscape a new lawn "inversely proportional" to the number of gardner working. That is more number of gardner working will take less time.

- The time taken by (n) number of gardner to complete the landscape (x) as per "inverse relationship" is given by the following formulation:

1 / x = Sum (1 / ti)

Where, i denotes the time for nth gardner.

- We have two gardner then the relationship becomes:

1 / x = 1 / t1 + 1/t2

- Solve for x:

x = (t1*t2) / (t1 + t2)

x = (45*36) / ( 45 + 36 )

x = 20 hrs

- It will take 20 hrs to landscape of lawn if two garnders work together.