To solve this problem, we need to determine the value of x, which represents the length of time Polly stands on her back legs compared to Pulsar.
Let's break down the information given:
Length of time Pulsar stands on his back legs: 10 minutes
Length of time Polly stands on her back legs: x * (length of time Pulsar stands on his back legs)
Length of time Petra stands on his back legs: 1/6 * (length of time Polly stands on her back legs)
Combined length of time the three entertainers stand on their back legs: 45 minutes
We can set up the equation as follows:
Length of time Pulsar stands on his back legs + Length of time Polly stands on her back legs + Length of time Petra stands on his back legs = Combined length of time the three entertainers stand on their back legs
10 + x * 10 + (1/6) * (x * 10) = 45
Let's simplify and solve for x:
10 + 10x + (1/6) * 10x = 45
10 + 10x + (10/6)x = 45
To simplify the equation, we find a common denominator for 10 and 6:
10 + (60/6)x + (10/6)x = 45
10 + (70/6)x = 45
To isolate x, we subtract 10 from both sides of the equation:
10 + (70/6)x - 10 = 45 - 10
(70/6)x = 35
To solve for x, we multiply both sides of the equation by 6/70:
((70/6)x)(6/70) = 35(6/70)
x = 3
The value of x is 3.
#### 3
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Pulsar, the shuffle-dancing bear, Polly, the pink prancing poodle, and Petra, the proud portly pachyderm, are entertainers at the Big Top Circus.  In one show, Pulsar stands on his two back legs for a total of 10 minutes.  Then, Polly stands on her back legs for x times as long as Pulsar.  And then, finally, Petra stands of his back legs for one-sixth as long as Polly.  What is the combined length of time, in minutes, The three entertainers stand on their back legs 45 times.

### Answer:
