QuestionOne work was done by team 1 in 10 days and team 2 in 15 days. If we cooperate, how many days will the work be done?

Studdy Solution

STEP 1

1. Team 1 completes the work in 10 days.
2. Team 2 completes the work in 15 days.
3. The work rate of each team is constant.
4. We are seeking the combined work rate of both teams working together and the total time needed to complete the work.

STEP 2

1. Determine the individual work rates for Team 1 and Team 2.
2. Calculate the combined work rate when both teams work together.
3. Use the combined work rate to find the total time needed to complete the work.

STEP 3

Calculate the work rate of Team 1. The work rate is the fraction of the work done per day. $\text{Work rate of Team 1} = \frac{1 \text{ work}}{10 \text{ days}} = \frac{1}{10} \text{ work/day}$

STEP 4

Calculate the work rate of Team 2. Similarly, the work rate is the fraction of the work done per day. $\text{Work rate of Team 2} = \frac{1 \text{ work}}{15 \text{ days}} = \frac{1}{15} \text{ work/day}$

STEP 5

Add the individual work rates to get the combined work rate when both teams work together. $\text{Combined work rate} = \frac{1}{10} + \frac{1}{15}$

STEP 6

Find a common denominator and add the fractions to calculate the combined work rate. $\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \text{ work/day}$

STEP 7

Determine the total time needed to complete the work using the combined work rate. $\text{Total time} = \frac{1 \text{ work}}{\frac{1}{6} \text{ work/day}} = 6 \text{ days}$
Solution: The work will be completed in 6 days when both teams cooperate.

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