It takes one man one day to dig a 2m x 2m x 2m hole. How long does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?
x = rate of one man = 23 m3/ 1 day = 8m3/day
3x = rate of three men = 3(8m3/day) = 24m3/day
64m3/(24m3/day) = 2 2/3 days
Is this correct?
Yes, your calculations are correct. To find the rate at which three men can dig a hole, you first find the rate at which one man can dig, which is 8m3/day. Then you multiply this rate by 3 to get the rate at which three men can dig, which is 24m3/day.
To find out how long it takes three men to dig a 4m x 4m x 4m hole, you divide the volume of the hole (64m3) by the rate at which three men can dig (24m3/day).
64m3 / 24m3/day = 2.67 days
So, it will take approximately 2 2/3 (or 2.67) days for three men working at the same rate to dig a 4m x 4m x 4m hole.