Q. 225 It takes two hours for two machi... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 225 (page 920)

It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture 10,000 parts alone?

Short Answer

Expert verified

The time take by machine 2 is $4.6 h$ and by machine 1 is $3.6 h$

Step by step solution

Step 1. Given Information

The given data is it takes 2 hours for two machines to manufacture. Machine 1 do the job alone in 1 hour less than machine 2.

Step 2. Calculation

Let the time taken by machine 2 is $t h o u r s$ ,

Use the given information to complete the table.

Type	No. of hours needed to complete the job	Part of job completed per hour.
Machine 1	$t - 1$	$\frac{1}{t - 1}$
Machine 2	$t$	$\frac{1}{t}$
Together	2	$\frac{1}{2}$

Since, the part completed by machine 1 plus the part completed by machine 2 equals to the amount completed together. So, we get,

$\frac{1}{t} + \frac{1}{t - 1} = \frac{1}{2}$

Solve the equation to find the value of time,

$2 t (t - 1) (\frac{1}{t} + \frac{1}{t - 1}) = \frac{1}{2} (2 t) (t - 1) 2 t - 2 + 2 t = t^{2} - t t^{2} - t - 4 t + 2 = 0 t^{2} - 5 t + 2 = 0$

Use the quadratic formula to simplify further.

$t = \frac{- 5 卤 \sqrt{{(- 5)}^{2} - 4 (1) (2)}}{2 (1)} t = \frac{5 卤 \sqrt{17}}{2} t 鈮� 0.4, 4.6$

Because the $0.4 h$ does not make any sense so we will discard this value and consider the another one.

Thus, time taken by machine 2 is $4.6 h$ and machine 1 is $4.6 - 1 = 3.6 h$

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91影视

It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture 10,000 parts alone?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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