Question

Caleb can work 2/5 times as fast as Charlie and Cameron work together,Caleb and Cameron work together two times as fast as Charlie . if Cameron takes 25 days to complete a task, working alone then how long would Charlie would take to complete a same task, working alone ? ​

Answer 1

Answer:

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Answer 2

Charlie will take $21\frac{7}{8}$  days to complete the same task, working alone.

Given:

• Caleb can work 2/5 times as fast as Charlie and Cameron work together.
• Caleb and Cameron work together two times as fast as Charlie.
• Cameron takes 25 days to complete a task.

To find:

The time Charlie would take to complete a same task, working alone.

Solution:

• 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= $\frac{2}{5}$(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= $\frac{2}{5}$(x+25)  and y+25=2x ⇒ y=2x-25    

Solving above for the values of x.

2x-25= $\frac{2}{5}$(x+25)

⇒ 10x-125=2x+50

⇒ 10x-2x=125+50

⇒8x = 175

⇒x = $\frac{175}{8}$

⇒x= $21\frac{7}{8}$

Hence,Charlie will take $21\frac{7}{8}$  days to complete a same task, working alone.

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