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Tina D.
Math and Science Tutor for 16 years
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Pre-Calculus
TutorMe
Question:

https://www.dropbox.com/s/3txk1eydpgfu2s0/pre-calculus%20question.pdf?dl=0

Tina D.

https://www.dropbox.com/s/ezvyutypjmiajpk/pre-calculus%20solution.pdf?dl=0

Geometry
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Question:

https://www.dropbox.com/s/zknhxc5jjh9j4hf/geometry%20%20question.pdf?dl=0

Tina D.

https://www.dropbox.com/s/x4530ru9jjv3g85/solution%20to%20geometry%20question.pdf?dl=0

Algebra
TutorMe
Question:

Working together, Sebastian and Joaquin can paint a house in 12 days. If Sebastian works alone and then joined by Joaquin after 4 days, it took them another 10 days to complete the job. How long will it take each of them to finish the whole job if they worked alone?

Tina D.

Let: X - the number of days it would take Sebastian to finish the whole painting job alone. Y - the number of days it would take Joaquin to finish the whole painting job alone. 1/X - the rate at which Sebastian can do the job alone; this is the amount or the fraction of the painting job, done by Sebastian per day. 1/Y - the rate at which Joaquin can do the job alone; this is the amount or the fraction of the painting job, done by Joaquin per day. Working together, it would take them 12 days to finish the whole painting job, so we let 1/12 - a rate at which Sebastian and Joaquin can finish the whole painting job together. Therefore, adding their rates together: 1/X + 1/Y = 1/12 ( equation 1 ) Now let our working equation be: (amount of job done by Sebastian alone in 4 hours) + ( amount of job done by Sebastian and Joaquin in the 10 hours) = 1 whole painting job ( equation2 ) Given that Sebastian had already worked for days before Joaquin joined him, we solve for the amount of painting job Sebastian had finished in 4 days. rate = (amount of job done) / (amount of time spent to do the job ) so, amount of job done = (rate) × ( amount of time spent to do the job). Plugging in, amount job done by Sebastian = ( 1/X) × (4) = 4/X Joaquin joined Sebastian, and together they completed the remaining job in 10 more days. We also solve for the amount of job done by them working together for 10 days. we know that working together, their rate is 1/12 so, amount of job done by Sebastian and Joaquin = ( 1/12 ) × ( 10) = 10/12 or 5/6 of the total painting job to be done. Plugging in all these to equation 2, 4/X + 5/6 = 1 we solve for X: 4/X + 5/6 = 1 4/X = 1 － 5/6 4/X = 1/6 cross multiplying, we have X = 24 Solving for Y, we plug in X = 24 to equation 1 : 1/X + 1/Y = 1/12 1/24 + 1/Y = 1/12 1/Y = 1/12 － 1/24 1/Y = 1/24 cross multiplying, we have Y = 24 it would take Sebastian 24 days to finish the whole painting job alone. it would take Joaquin 24 days to finish the whole painting job alone.

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