Ignore swell and shrinkage for this problem.
An excavator with a 5 cubic yard bucket has a cycle time of 33 seconds. The trucks you have available can be filled in 3 cycles of the excavator (trucks have 15 cubic yards capacity). The trucks take 5 minutes to haul, 45 seconds to dump, and 3 minutes to return to the excavator.
a. Find the number of trucks to balance the output of the excavator. Report your answer to at least 1 decimal place. You can assume 60 minute hours.
b. If you round up the number of trucks, what is the output per 60 minutes?
c. If you round the number of trucks down, what is the output per 60 minutes?

(a) 5.3

(b) 6

(c) 5

Explanation:

First we calculate time required for excavator to fill 1 truck:

Time to Fill 1 Truck = (No. of Cycles To Fill)(Cycle Time)

Time to Fill 1 Truck = (3)(33 sec)

Time to Fill 1 Truck = 99 sec

Now, we find the time taken by a truck to come back to excavator, after dumping:

Time of Return = Hauling Time + Time to Dump + Time to Come Back

Time of Return = 5 min + 45 sec + 3 min

Time of Return = 300 sec + 45 sec + 180 sec

Time of Return = 525 sec

(a)

In order to balance the output of excavator with number of trucks, following condition must be satisfied:

Time of Return = (No. of Trucks)(Time to Fill 1 Truck)

525 sec = (No. of Trucks)(99 sec)

No. of Trucks = 525 sec/99 sec

No. of Trucks = 5.3

(b)

If we round up the number of trucks, we get:

No. of Trucks = 6

(c)

If we round down the number of trucks, we get:

No. of Trucks = 5

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