The number of days that it will take Charles to complete the work alone is: 21⁷/₈ days
How to solve Algebra Word problems?
Let x be the number of days charlie takes to complete the work alone.
Let y be the number of days Caleb takes to complete the work alone.
Let z be the number of days Cameron takes to complete the work alone.
Caleb can work 2/5 times as fast as Charlie and Cameron work together.
Mathematically we can write it as y = ²/₅(x + z) ...(I)
Caleb and Cameron work together two times as fast as Charlie.
Mathematically we can write it as:
y + z = 2x ...(II)
Cameron takes 25 days to complete a task.
z = 25 ...(III)
Putting the value of (III) in (I) and (II) we get,
y = ²/₅(x + 25)
and y + 25 = 2x
⇒ y = 2x - 25
Solving above for the values of x.
2x - 25 = ²/₅(x + 25)
⇒ 10x - 125 = 2x + 50
⇒ 10x - 2x = 125 + 50
8x = 175
x = 21⁷/₈ days