Question

1. Mark can build a cage by himself for 3 days. Carl can build the same cage in 6 days. How long would it take them if they worked together?
2. Jim can type a research report in 5 hours. Emma who is slower typist, help Jim and work together. They finished the report in 3 hours. How long would it take Emma to finish the research report if she had worked alone?

Answer 1

Answer:

1. 12. 2.2

Step-by-step explanation:

1.Do HCF 2. Subtract 5-3=2.

Answer 2

Given:

1. No. of days required for Mark to build cage = 3

No. of days required for Carl to build cage = 6

2. No. of hours required for Jim to type = 5

No. of hours required for Emma and Jim to type together = 3

To find:

1. No. of days required for Mark and Carl to work together.

2. No. of hours required for Emma to type.

Solution:

1. Let the rate at which Mark can build cage in one day be M and the rate at which Carl can build cage in one day be C. Total amount of work both of them can do together in one day:

$\frac{1}{D} = \frac{1}{3}+\frac{1}{6}$

where D is the no. of days both of them can complete the cage.

Taking the LCM of 3 and 6, we get LCM = 6

$\frac{1}{D} = \frac{1}{3}*\frac{2}{2}+\frac{1}{6}*\frac{1}{1}$

$\frac{1}{D} = \frac{2+1}{6} = \frac{3}{6}=\frac{1}{2}$

Hence, 2 days are required for Mark and Carl to work together to complete the cage.

2. Let the rate at which Jim can type in one hour be J and the rate at which Emma can type in one hour be E. Total amount of work both of them can do  together for one day:

$\frac{1}{3}=\frac{1}{5}+\frac{1}{E}$

$\frac{1}{3} -\frac{1}{5}=\frac{1}{E}$

Taking the LCM of 3 and 5, we get LCM = 15

$\frac{1}{3}*\frac{5}{5}-\frac{1}{5}*\frac{3}{3}=\frac{1}{E}$

$\frac{5-3}{15}=\frac{1}{E}$

$\frac{1}{E}=\frac{2}{15}$

$E=\frac{15}{2}=7.5$ hours

Hence, Emma requires 7.5 hours to type the report alone.

1. 2 days are required for Mark and Carl to work together to complete the cage.

2. Emma requires 7.5 hours to type the report alone.