Chapter 12.1, Problem 36STP

To determine

To find: the number of hours after when Carlos and Cecelia have same number of problems.

Answer to Problem 36STP

  $1.2\text{hours }$ .

Explanation of Solution

Given:

The rate at which Carlos solved the problem is $25\text{ question per hour}$ .

And the rate at which Cecelia solved the problem is $30\text{ question per hour}$ .

Calculation:

According to the question, Carlos started 12 min before Cecelia.

Therefore, when Cecelia worked for 1 hour, then Carlos worked for 1 hours and 12 min.

Now, total number of problems solved by Carlos worked in 1 hours and 12 min:

  $\begin{array}{l}1\text{ hours}\to \text{25 question}\\ \therefore \text{60min}\to 25\text{ question}\\ \therefore \text{1min}\to \frac{25}{60}\text{ question}\\ \therefore \text{12min}\to \frac{25}{60}\times \text{12 question}\\ \Rightarrow \text{12min}\to 5\text{ question}\\ \therefore 1\text{ hours 12min}\to 25+5=30\text{ question}\\ \Rightarrow 1\text{ hours 12min}=1+\frac{12}{60}=1+\frac{1}{5}=1.2\text{hours }\end{array}$

At the same time, Cecelia solved the 30 problem.

Hence, after $1.2\text{hours}$ , Carlos and Cecelia have same number of problems.