Question

Dean and his younger brother sam are digging a hole to make imu for the luau. Working together it takes them 1.5 hours to finish the hole. If it would take sat twice as long to finish the hole working alone as it would dean how long would it take dean if he had to dig the hole by himself?

Answer 1

Let's start by finding out how much of the job each person can do in one hour.

Dean and Sam can do the job in 1.5 hours, so their combined hourly rate is:

1 job / 1.5 hours = 0.67 jobs per hour

Let's call Dean's hourly rate "D" and Sam's hourly rate "S". We can use this information to set up two equations:

D + S = 0.67 (the combined hourly rate)
S = 2D (it takes Sam twice as long as Dean to do the job alone)

Now we can substitute the second equation into the first equation to solve for D:

D + 2D = 0.67
3D = 0.67
D = 0.22

So Dean can do 0.22 jobs per hour. To find out how long it would take him to do the job alone, we can use the formula:

time = jobs / rate

time = 1 job / 0.22 jobs per hour = 4.55 hours

So it would take Dean 4.55 hours to dig the hole by himself.