Question

You have a huge review project for English where you have to answer 300 questions. You start on it after school at 5:00. At 6:30, you have answered 55 questions.What time will you finish your assignment if you don't take any breaks?The linear equation represents Q questions remaining after h hours working on the homework.Q=-110/3h+300

Answer 1

assignmentYou have to answer 300 questions.

You start at 5:00 and by 6:30 you have answered 55 questions. → the time that passed by is one hour and 30 minutes. To make the calculations easier I will express the time in minutes.

1 hour has 60 minutes, so 1 hour and 30 minutes has a total of 60+30=90 minutes

So, in 90minutes, 55 questions were answered.

Considering that the timer per question answered follows the same rate, you can use cross multiplication to determine how much time it will take to answer the 300 questions:

55 questions _____ 90 minutes

300 questions ____ x minutes

`\begin{gathered} (90)/(55)=(x)/(300) \\ x=300\cdot((90)/(55)) \\ x=490.90\approx491 \end{gathered}`

It will take you 491 minutes to answer all questions.

Now you have to express the minutes as hours, for this, divide 491 by the number of minutes in 1 hour (i.e. 60 minutes)

`(491)/(60)=8.18`

This indicates that it will take a little more than 8 hours to finish the questions.

If you multiply the decimals "0.18" by 60 you'll get the number of minutes

`0.18\cdot60=10.8\approx11\min`

So it will take 8 hours and 11 minutes to solve the 300 questions.

If you start answering at 5:00 without any break, add the time calculated to determine the time you will finish the assignment:

`5\colon00+8\colon11=13\colon11`

You will finish the assignment at 13:11

Given the linear function that represents the remaining questions, Q, after h hours of work

`Q=-(110)/(3)h+300`

You have to determine how much time it will take to finish the assignment, that is, the value of h for Q=0 (no questions remaining), you have to equal the equation to zero

`0=-(110)/(3)h+300`

Now you have to calculate the value of h, first, subtract 300 from both sides of the equation

`\begin{gathered} 0-300=-(110)/(3)h+300-300 \\ -300=-(110)/(3)h \end{gathered}`

Next, you have to divide the equation by -110/3 to reach the value of h, or since it is a fraction, you can multiply both sides of the equation by the reciprocal (inverse) fraction -3/110

`\begin{gathered} (-300)(-(3)/(100))=(-(110)/(3))(-(3)/(100))h \\ (90)/(11)=h \end{gathered}`

The time it takes to solve all 300 questions is h=90/11 hours or expressed as a decimal value 8.18 hours