Multiple choice

The distance between points P and Q is 108 miles. Two joggers start running from P and Q simultaneously toward each other. The jogger who starts from P runs at a constant speed of 6 miles per hour. Meanwhile, the other jogger runs with varying speeds: in the first hour, the speed is 4 miles per hour; in the second hour, it is 5 miles per hour; in the third hour, it is 6 miles per hour; and so on. When will they meet each other?

  1. 48 miles away from P

  2. 32 miles away from Q

  3. After 18 hours from the start

  4. After 5 hours from the start

  5. Midway between P and Q
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Jogger 1 (from P) speed = 6 mph. Jogger 2 (from Q) speeds: 4, 5, 6, 7, 8... Distance covered by J2 in n hours is the sum of an arithmetic progression: n/2 * (2*4 + (n-1)*1) = n/2 * (n+7). Total distance = 6n + n/2 * (n+7) = 108. Multiplying by 2: 12n + n^2 + 7n = 216, so n^2 + 19n - 216 = 0. Factoring: (n+27)(n-8) = 0. They meet after 8 hours. Distance from P = 6 * 8 = 48 miles.

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