It takes an older employee 13 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 10 hours. how long will it take them to clear the walk if they work together?

Work in rates per hour. These rates can then be added to form an equation

1/13 + 1/10 = 1/x where x is the time for both working together

multiply thru by 130x:-

10 x + 13 x = 130

x = 130/23 = 5.65 hours or about 6 hours 39 minutes