Jack can paint a wall in 5 hours and John can paint the same wall in 6 hours. If they work together, how long would it take for both of them to finish the job?
Possible answers: 2h 18min, 2h 44min, 3h 5min, 3h 40min, 4h 6min
My solution:
rate of Jack= 1/5
rate of John=1/6
Total: 1= 1/5t+ 1/6t
t=30/11 which is 2.72 which I think is 3h and 2min
But the answer is 2h and 44min and I'm not sure why
To convert 2.72 hours to minutes, we can multiply by 60 to get 163.2 minutes. Rounding to the nearest minute, we get 163 minutes, which is equivalent to 2 hours and 43 minutes. Therefore, the answer of 2 hours and 44 minutes is the closest option to our calculated time of 2.72 hours.
The answer of 2 hours and 44 minutes is correct. Let's go through the calculation step-by-step:
First, we need to assign a variable for the time it takes for both Jack and John to complete the job together. Let's call this variable t.
Next, we can create an equation based on the rates at which Jack and John paint the wall:
Rate of Jack = 1/5 walls per hour
Rate of John = 1/6 walls per hour
When they work together, their rates add up, so the equation becomes:
1/5t + 1/6t = 1
Now we can solve for t. To do this, we need to find a common denominator for the fractions:
(6/30)t + (5/30)t = 1
Simplifying the equation:
(11/30)t = 1
To solve for t, we multiply both sides of the equation by the reciprocal of 11/30, which is 30/11:
(11/30)t * (30/11) = 1 * (30/11)
t = 30/11
Converting 30/11 into a mixed number gives us:
t ≈ 2.727 hours
To express this time in hours and minutes, we can multiply the decimal part (0.727) by 60 to convert it into minutes:
0.727 * 60 ≈ 43.6 minutes ≈ 44 minutes
Therefore, the total time it takes for both Jack and John to finish the job working together is approximately 2 hours and 44 minutes.