Question

A teacher wants to make a test containing $20$verbal and $30$math questions. Each verbal
question is to be allotted $45$seconds to complete and each math question is to be given
$1$minute $20$seconds. How many minutes should she allow for the whole test?

Answer 1

Hint: Convert the time in seconds to minutes by dividing it by $60.$ Multiply the time
required for one question with the total number of questions. Add both the time durations.
Complete step-by-step answer:
In the given problem, the test contains $20$verbal and $30$math questions.
Number of verbal questions is$20$.
Number of math questions is $30$.
To answer the questions, the teacher allotted various time duration to the students. The students
need to answer the question in the allotted time interval only.

The teacher allots a time interval of $45$seconds to answer the verbal question and$1$minute
$20$seconds for the math question.
First convert $45$seconds to minutes:
To do the above operation, divide by $60.$
$45$seconds
$\begin{array}{l} = \dfrac{{45}}{{60}}\\ = \dfrac{3}{4}\,{\rm{minutes}}\end{array}$
Hence, the time interval for one verbal question comes out to be
$\dfrac{3}{4}\,{\rm{minutes}}$.
Since, the total number of verbal questions is $20$.
So, the time required to complete all the verbal questions is:
$\begin{array}{c} = 20 \times \dfrac{3}{4}\\ = 5 \times 3\\ =
15\,{\rm{minutes}}\end{array}$
Secondly, convert $1$minute $20$seconds to minutes:
To do the above operation, divide $20$by $60.$
$1$ minute $20$seconds
$\begin{array}{l} = 1 + \dfrac{{20}}{{60}}\\ = 1 + \dfrac{1}{3}\\ = \dfrac{4}{3}{\rm{
minutes}}\end{array}$
Hence, the time interval for one math question comes out to be
$\dfrac{4}{3}\,{\rm{minutes}}$.
Since, the total number of verbal questions is$30$.
So, the time required to complete all the math questions is:
$\begin{array}{c} = 30 \times \dfrac{4}{3}\\ = 10 \times 4\\ =
40\,{\rm{minutes}}\end{array}$
Hence, the total time required to solve the verbal and the math questions is:
$\begin{array}{l}\left( {40 + 15} \right){\rm{ minutes}}\\{\rm{ = 55 minutes}}\end{array}$
Note: In this problem you are asked to find out the total time required to answer all the
questions. So, while solving the questions, first convert the time duration into seconds. You
can also convert it to minutes. If you do so, convert the other time duration in minutes too.