Run a marathon

Algebra Level 2

Illyr is practicing for a marathon. In the first practice, he starts to run for $\text{30 m}$ . The second practice he runs $\frac 65$ times the distance on the first practice $(\text{30 m})$ . The third practice he runs $\frac 65$ times the distance on the second practice and so on.

What is the total distance Illyr has run if he does this practice for 12 times?

1187.415 \text{ m}

1082.219 \text{ m}

\text{98.2194 m}

\text{432.000 m}

Infinity

2 solutions

Chew-Seong Cheong
Oct 30, 2019

The total distance Illyr has run for practicing 12 times is given by:

$\begin{aligned} D & = 30 \blue{\left(1+\frac 65 + \left(\frac 65\right)^2 + \cdots + \left(\frac 65\right)^{11}\right)} & \small \blue{\text{Sum of a geometric progression}} \\ & = 30 \blue{\left(\frac {\left(\frac 65\right)^{12}-1}{\frac 65 - 1}\right)} \\ & \approx \boxed{1187.415} \end{aligned}$

Reference: Geometric progressions

Were the answer choices changed?? This is how I did this problem the other day but I recall the correct answer not being an option and I got it wrong for choosing the one that was closest.

Tristan Goodman - 1 year, 7 months ago

Yes, they were changed. @NIckolas Kpaj mentioned the changes in the problem and I changed the answer options.

Chew-Seong Cheong - 1 year, 7 months ago

Callie Ferguson
Oct 30, 2019

This one was a bit difficult because of the incorrect answer choices; might be easier to just make a new problem and link that to this one.

This a java program solution:

public class MyClass

{

public static void main(String args[])

{

    double distance = 30;

    double total_distance = 0;

    int runs = 12;

    for (runs=12;runs>=1;)

    {

        total_distance+=distance;

        distance*=1.2;

        runs--;

    }

    System.out.println(total_distance);

}

}

the output gives us the solution.

Karthikeya Kakarlapudi - 1 year, 7 months ago

Run a marathon

2 solutions

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