Question

Diego, a fitness enthusiast, decides to maintain an average of 10 minutes per day on a treadmill for the April. His average run for the first 15 days was 9.4 minutes and for the next 10 days was 8.1 minutes. What is the daily running that he needs to do to achieve his target in the remaining days?

• A. 13.2 minutes
• B. 17.8 minutes
• C. 14.6 minutes
• D. 15.6 minutes

Answer 1

The correct option is D 15.6 minutes

April has a total of 30 days.
For the first 15 days, his average run was 9.4 minutes.

April 1st to April 15th:
$\frac{{\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{15}}{15}=9.4$

${\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{15}=9.4\times 15$
${\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{15}=141$ minutes

For the next 10 days, his average run was 8.1 minutes.

April 16th to April 25th:
$\frac{{\text{D}}_{16}+{\text{D}}_{17}+.......+{\text{D}}_{25}}{10}=8.1$

${\text{D}}_{16}+{\text{D}}_{17}+.......+{\text{D}}_{25}=8.1\times 10$
${\text{D}}_{16}+{\text{D}}_{17}+.......+{\text{D}}_{25}=81$ minutes

Let the total run for the next 5 days $=x$

We can write the durations for different durations of the month as:

Run for first 15 days + Run of next 10 days + Run for last 5 days = Total expected run

Average for the entire month
$=10$ minutes

$\frac{{\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{30}}{30}=10$

${\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{30}=10\times 30$
${\text{D}}_1+{\text{D}}_2+.......+{\text{D}}_{30}=300$ minutes

$141+81+x=300$
$222+x=300$
$x=300-222$
$x=78$ minutes

To maintain the average of 10 minutes, Diego has to run $\frac{78}{5}=15.6$ minutes every day for the remaining 5 days.