Question

It takes an older employee 14 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 9 hours. How long will it take them to clear the walk if they work together?It will take them ___hour(s) ___minute(s) to clear the walk if they work together.If needed, round answer to 1 decimal places.Enter DNE for Does Not Exist, oo for Infinity

Answer 1

Let's say A is the amount of snow they shovel from that sidewalk. Then, the velocity in which the older employee shovels A is:

A/14

Now, the velocity in which the younger employee shovels A is

A/9

Now, let's call t the time they take to shovel the sidewalk together. Then, if we multiply the velocity of the older employee by t, we have the amount Ao that the older one will shovel:

Ao = t*A/14

Similarly, the amount Ay that the younger one will shovel is:

Ay = t*A/9

Continuing, we know that Ao and Ay must sum up to A, because each of them is a part of the total amount A:

Ao + Ay = A

Then, using the expressions for Ao and Ay in the last equation, we find:

Ao + Ay = A

t*A/14 + t*A/9 = A

A* (t/14 + t/9) = A

t/14 + t/9 = A/A

t/14 + t/9 = 1

(9 + 14)t/126 = 1

23t = 126

t = 126/23

t ≅ 5.478

t ≅ 5h + 0.478h

t ≅ 5h + 0.478*60 min (because 1 hour = 60 minutes)

t ≅ 5h + 28.7 min

Therefore,

It will take them 5 hours 28.7 minutes to clear the walk if they work together.