Shanice can dig a 10 ft by 10 ft hole in ten hours thus her rate is 1/10 holes per hour

Mary can dig the same hole in seven hours thus her rate is 1/7 holes per hour

let x = represent the hours they need to dig the hole together

the together rate is 1/x holes per hour

1/10 + 1/7 = 1/x

by solving we find

x = 70/17

x = 4 2/17 hr

x = 4 hr 2*60/17 min

x = 4 hr 7.1 min

x = 4.1 hr approximately

click here to see the step by step solution of the equation

Click to see all the steps

it would take them 4.1 hours approximately to dig the hole together.