Rate of Work Problems?

Question

A small gas generator runs for 4 hours on a tank of propane. A larger sized generator runs for only 3 hours on the same sized tank of propane. Power from both generators is required for an outdoor concert. How long will the generators run if both are attached to the same tank?

Answer 1

P1 = smaller generator's rate of energy consumption
P2 = larger generator's rate of energy consumption
t = time it takes to deplete the tank
E = energy available in new tank to be consumed

Because there is a fixed amount of energy in each tank to begin with, you know that the energy consumed by just the smaller generator in 4 hours is equal to the energy consumed by the LARGER generator in 3 hours...mathematically:

4·P1 = 3·P2 ──► P1 = 3/4·P2
P1 + P2 = 3/4·P2 + P2 = 7/4·P2

Now, when we hook both generators to a single tank, both generators will stop consuming energy at the same moment (that is, when the tank runs out of propane):

t·P1 + t·P2 = 3·P2
(as before, 3·P2 is the amount of energy in a new tank; you could also use 4·P1)

t·(P1 + P2) = 3·P2
t = 3·[P2 / (P1 + P2)]
= 3·[P2 / (7/4·P2)]
= 12 / 7 = 1+5/7 hours

Answer 2

In 1 hour the small generator consumes 1/4th part of propane
In 1 " " larger " " 1/3 " " '
Hence together they consume in 1 hour (1/4 +1/3 or )7/12 parts
Hence if both of them are connected to the same tank,they would run for (1)/(7/12) or 12/7 or 1 5/7 hours
"

Answer 3

The small generator uses 1/4 tank per hour, the large uses 1/3 tank per hour, so together they use 7/12 tank per hour, and so 1 tank will last 12/7 = 1 5/7 hours = 102 6/7 minutes.

Answer 4

The smaller consumes 0.25 tank/hour. The larger consumes 0.33 tank/hour. Together they consume 0.58 tank/hr. The propane will last for 1.00 div by 0.58, or 1.71 hour.