Janet can shovel snow from her driveway in 55 min. Tom can do the same job in 30 min. How long would it taket Janet and Tom to shovel the driveway if they worked together?
To find out how long it would take Janet and Tom to shovel the driveway if they work together, we can use the concept of work rates.
Janet's work rate is 1 driveway per 55 minutes, which can be represented as 1/55 driveways per minute.
Tom's work rate is 1 driveway per 30 minutes, which can be represented as 1/30 driveways per minute.
To determine their combined work rate, we add their individual work rates together:
Combined work rate = Janet's work rate + Tom's work rate
Combined work rate = 1/55 + 1/30 driveways per minute
To calculate how long it would take them to shovel the driveway together, we can take the reciprocal of the combined work rate:
Time = 1 / (Combined work rate)
Time = 1 / (1/55 + 1/30) minutes
To simplify the calculation, we can find a common denominator for 55 and 30, which is 330:
Time = 1 / ((6/330) + (11/330)) minutes
Time = 1 / (17/330) minutes
To divide by a fraction, we multiply by the reciprocal:
Time = 1 * (330/17) minutes
Time ≈ 19.41 minutes
Therefore, it would take Janet and Tom approximately 19.41 minutes to shovel the driveway together.