Acme movers charges $50 plus $20 per hour to move household goods across town. Hank’s Movers charge $45 per hour. For what lengths of time does it cost less to hire Hank’s Movers?
45x<50 + 20x.
25x < 50,
X < 2 hours.
Well, it seems like we've stumbled upon a moving battle of epic proportions! Let me whip out my handy calculator and crunch some numbers for you.
For Acme movers, the cost is $50 plus $20 per hour. And for Hank's Movers, it's a straight $45 per hour.
To figure out when it costs less to hire Hank's Movers, we need to find the hours when the two prices are equal. Let's call that "x" for simplicity.
For Acme movers, the cost would be $50 + $20x.
For Hank's Movers, the cost would be $45x.
So, we can set up an equation:
50 + 20x = 45x
Let's solve that equation:
50 = 45x - 20x
50 = 25x
x = 2
Ah! So, it looks like if you plan on moving for 2 hours or less, it would be cheaper to hire Hank's Movers. Anything beyond 2 hours, and Acme movers take the lead.
Remember, this is all based on the numbers provided, so be sure to double-check with the companies for their most up-to-date rates. And don't forget to tip your movers, because they're doing all the heavy lifting!
To determine for what lengths of time it costs less to hire Hank's Movers, we need to compare the total cost of hiring Acme Movers with the total cost of hiring Hank's Movers for different lengths of time.
Let's assume the length of time for which we want to compare the costs is "t" hours.
For Acme Movers:
Total Cost = $50 (fixed charge) + $20 (hourly rate) * t
For Hank's Movers:
Total Cost = $45 (hourly rate) * t
Now, we need to find the break-even point where the cost of hiring Hank's Movers becomes less than the cost of hiring Acme Movers.
Setting the two equations equal to each other:
$50 + $20t = $45t
Simplifying the equation:
$20t - $45t = $50
-$25t = $50
t = $50 / -$25
t = -2
Based on this calculation, we can see that Hank's Movers become cheaper for negative lengths of time, which does not make sense in this context. Therefore, it is not possible for Hank's Movers to be cheaper than Acme Movers.
To determine for what lengths of time it costs less to hire Hank's Movers compared to Acme Movers, we need to set up an equation based on the given information.
Let's assume the number of hours needed to move household goods is represented by "t."
For Acme Movers, the cost can be calculated as follows:
Cost = $50 (fixed charge) + $20 (per hour charge) * t (number of hours)
For Hank's Movers, the cost can be calculated as follows:
Cost = $45 (per hour charge) * t (number of hours)
To find the lengths of time for which it costs less to hire Hank's Movers, we need to set up an inequality:
Cost of Hank's Movers < Cost of Acme Movers
$45t < $50 + $20t
Now, let's solve for "t":
$45t - $20t < $50
$25t < $50
t < $50 / $25
t < 2 hours
So, for lengths of time less than 2 hours, it costs less to hire Hank's Movers compared to Acme Movers.