SOLUTION: A new truck has arrived at Kroger. It takes Jimbo six hours to unload such a truck, while it takes Olaf ten hours to unload it. If Jimbo and Olaf work together, how long will it t

Question 508431: A new truck has arrived at Kroger. It takes Jimbo six hours to unload such a truck, while it takes Olaf
ten hours to unload it. If Jimbo and Olaf work together, how long will it take them to unload the truck?
Found 2 solutions by stanbon, lmeeks54:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A new truck has arrived at Kroger. It takes Jimbo six hours to unload such a truck, while it takes Olaf
ten hours to unload it. If Jimbo and Olaf work together, how long will it take them to unload the truck?
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Jimbo rate = 1/6 job/hr
Olaf rate = 1/10 job/hr
---
Together rate: 1/x job/hr
----
Equation:
1/6 + 1/10 = 1/x
Multiply thru by 30 to get:
5x + 3x = 30
8x = 30
x = 15/4 = 3 hr 45min (time to do the job alone)
==================================================
Cheers,
Stan H.
=================
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This is pretty straight forward. First calculate each workers truck-emptying rate. You want to add their rates since they will be working together. However, if their rates are fractions of an hour, you will have to find the lowest common denominator (LCD) so they can be directly added together.
* * * * *
Jimbo takes 6 hrs to unload a truck, or as a rate, he unloads 1/6 truck per hr
Olaf takes 10 hrs to unload a truck, or as a rate, he unloads 1/10 truck per hr
* * * * *
To see how much of a truck is unloaded per hr when they work together, we need to add the 1/6 per hr + 1/10 per hr to get a combined rate per hr...
* * * * *
But 1/6 + 1/10 doesn't easily add, so find the LCD for both (30)...
* * * * *
1/6 = 5/30
1/10 = 3/30
* * * * *
5/30 + 3/30 = 8/30, which is the combined unloading rate: .26667 trucks per hour
* * * * *
To find the total time in hrs, to unload one truck, take the inverse of the rate:
8/30 = the rate
30/8 = time to unload
* * * * * *
30/8 = 3.75 hrs
* * * * * *
Cheers,
Lee
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