An athlete prepares for the Comrades. He jogs out to a certain point and then turns back home. On the first day he turns after 6m.on the second day he turns after 10km. On the third day he turns after 14km.
1.after how many kilometres does he turn on the 7th day?
2.On which day did he jog 38km in total?
3how many kilometres has he jogged in total when he reached his house on the 10th day?
4.is it possible that this way of preparing for a race can carry on like this for an indefinite period of time?give a reason for your answer.
1. On the 7th day, he turns after 22km.
2. On the 5th day, he jogged 38km in total.
3. He has jogged a total of 90km when he reached his house on the 10th day.
4. No, it is not possible for this way of preparing for a race to carry on like this for an indefinite period of time. This is because the athlete would eventually reach a point where he would not be able to increase the distance he jogs each day, as it would become too strenuous for him.
1. To find out how many kilometers he turns on the 7th day, we need to identify the pattern. From the given information, we can deduce that the athlete is increasing the distance he jogs by 4 kilometers every day.
So, on the 7th day, he would turn back after 6 + (4 * 6) = 6 + 24 = 30 kilometers.
2. To determine on which day he jogged a total of 38 kilometers, we need to sum up the distances of all the previous days. We know that the athlete is increasing the distance by 4 kilometers each day.
To find which day he jogged a total of 38 kilometers, we can solve the equation: 6 + (10 + 14 + 18 + ... + n) = 38.
Using the formula for the sum of an arithmetic series, we can rewrite the equation as: 6 + ((n/2)(2*10 + (n-1)4)) = 38.
Simplifying the equation: 6 + (5n + 2n^2 - n) = 38.
Combining like terms: 6 + 4n + 2n^2 = 38.
Rearranging the equation: 2n^2 + 4n - 32 = 0.
Solving this quadratic equation will give us the value of n, representing the day on which he jogged a total of 38 kilometers.
3. To calculate the total distance he jogged when he reached his house on the 10th day, we need to sum up the distances of all the previous days.
Using the same pattern of increasing the distance by 4 kilometers each day, we can use the formula for the sum of an arithmetic series:
Total distance = (number of terms / 2) * (first term + last term)
In this case, the number of terms is 10 and the first term is 6. The last term can be calculated by multiplying the common difference (4 kilometers) by the number of terms (9) and adding it to the first term.
Total distance = (10/2) * (6 + (4 * 9)) = 5 * (6 + 36) = 5 * 42 = 210 kilometers
Therefore, when he reached his house on the 10th day, he had jogged a total of 210 kilometers.
4. It is not possible for this way of preparing for a race to carry on indefinitely. As per the given information, the athlete is increasing the distance by 4 kilometers each day. Eventually, there will be a limit on how far the athlete can jog before it becomes physically impossible to continue increasing the distance at this rate. The athlete would reach a point where the distance becomes unattainable or exceeds their physical capabilities. Therefore, this preparation method would not be sustainable in the long run.