It takes machine a x hours to manufacture a deck of cards that machine b can manufacture in y hours. if machine a operates alone for z hours and is then joined by machine b until 100 decks are finished, for how long will the two machines operate simultaneously?

The expression that shows how long the two machines will operate simultaneously is:

Step-by-step explanation:

We know that:

x: hours to manufacture a deck of cards for machine A

y: hours to manufacture a deck of cards for machine B

z: hours that machine A operates alone

The number of decks manufactured only by machine A is:

So, the remaining decks are given by:

Then, the combined rate of machines A and B would be:

The work-rate formula is:

Hence, the time that the two machines work simultaneously is:

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x