A person can plow out all the driveways on his street with his new four-wheel-drive truck in 4 hours. using a snow blade on a lawn tractor, his neighbor can plow out the same number of driveways in 10 hours. how long would it take them to do the work together?
To find out how long it would take them to do the work together, we can use the concept of work rates. Let's consider the work rate of the person with the new four-wheel-drive truck as "X" driveways per hour and the work rate of the neighbor with the lawn tractor as "Y" driveways per hour.
According to the problem, the person with the truck can plow out all the driveways on his street in 4 hours. So, we can say that his work rate is 1/4 driveways per hour, which means he can complete 1 driveway in 4 hours.
Similarly, the neighbor with the lawn tractor can plow out the same number of driveways in 10 hours, implying his work rate is 1/10 driveways per hour or he can complete 1 driveway in 10 hours.
Now, to determine how long it would take them to do the work together, we need to find the combined work rate when they work together, which we can calculate by adding their individual work rates.
Work rate when they work together = X + Y driveways per hour.
Since we know that the person with the truck can complete 1 driveway in 4 hours, his work rate is 1/4 driveways per hour.
Similarly, the neighbor's work rate is 1/10 driveways per hour.
Adding the two work rates, we get:
1/4 + 1/10 = 10/40 + 4/40 = 14/40 = 7/20 driveways per hour.
Therefore, when they work together, their combined work rate is 7/20 driveways per hour, meaning they can complete 7 driveways in 20 hours.
To find out how long it would take them to complete all the driveways, we can use the formula:
Time = Total work / Combined work rate
Since the total work is 7 driveways, the combined work rate is 7/20 driveways per hour. Plugging these values into the formula, we get:
Time = 7 driveways / (7/20 driveways per hour)
Time = 140 hours / 7
Time = 20 hours.
Hence, it would take them 20 hours to complete the work together.
c = combined time
they each do a fraction of the work
... the fractions add to one...the whole job
(c / 4) + (c / 10) = 1
20 is the common denominator ... (5c / 20) + (2c / 20) = 1
5c + 2c = 20 ... c = 20 / 7