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SCORPION-xisa [38]
3 years ago
6

A shoe repairman is working with his assistant, who takes 1.5 times as long to repair a pair of shoes. Together they can fix 20

pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
7 0

Answer: \dfrac{2}{3}\text{ hour}

Step-by-step explanation:

Let x be the time taken by the shoe repairman to repair 20 pairs of shoes and 1.5 x be the the time taken by his assistant to repair the shoes.

Since they took 8 hours to complete the whole job , so we have the following equation:-

\dfrac{1}{\text{Time taken by shoes repairman}}+\dfrac{1}{\text{Time taken by assistant}}=\dfrac{1}{8}\\\\ \dfrac{1}{x}+\dfrac{1}{1.5x}=\dfrac{1}{8}\\\\ \dfrac{1+1.5}{1.5x}=\dfrac{1}{8}\\\\ x=\dfrac{8\times2.5}{1.5}=\dfrac{40}{3}

i.e. Time taken by shoe repairman to repair 20 pairs of shoes  = \dfrac{40}{3}\text{ hours}

By unitary method ,

Then, Time taken by shoe repairman to repair 1 pair of shoes  = \dfrac{40}{3}\div 20\text{ hours}

=\dfrac{40}{3}\times\dfrac{1}{20}=\dfrac{2}{3}\text{ hour}

Hence, Time taken by shoe repairman to repair 1 pair of shoes =\dfrac{2}{3}\text{ hour}

lions [1.4K]3 years ago
5 0
Suppose the time taken for the repairman to fix one pair of shoes is x, time taken by the assistant will be 1.5x. 
The number of shoes repaired by shoe man in an hour will be:
1/x 
the number of shoes prepared by assistant in 1 hour will be:
1/1.5x
the number of shoes repaired by both of them in 1 hour will be:
8/20
hence;
1/1.5x+1/x=8/20
2.5/(1.5x)=2/5
cross-multiplying our equation we get:
2.5*5=1.5x*2
7.5=3x
x=7.5/3
x=2.5 hours
therefore we conclude that it takes the repairman 2.5 hours to fix one pair of shoes.


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X+y=3 x=6-4y using substitution
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4 0
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Read 2 more answers
For the following hypothesis test, H0: μ ≥ 150Ha: μ < 150​the test statistic a. must be positive. b. must be negative. c. can
Virty [35]

Answer:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

And since we are conducting a lower unilateral lest  then we expected that the value for the statistic would be negative. And the correct answer would be:

b. must be negative

Step-by-step explanation:

Data given and notation      

\bar X represent the sample mean    

s represent the standard deviation for the sample      

n sample size      

\mu_o =150 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is lower than 150, the system of hypothesis would be:      

Null hypothesis:\mu \geq 150      

Alternative hypothesis:\mu < 150      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

And since we are conducting a lower unilateral lest  then we expected that the value for the statistic would be negative. And the correct answer would be:

b. must be negative

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