Question

Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)

Answer 1

Bob takes 26 seconds to run one lap of the track.

Step-by-step explanation:

To find the time it takes for Bob to run one lap of the track, we need to determine his speed. Since Bob and Akira pass each other for the first time after 26 seconds, we can consider this as the time it takes for them to cover a combined distance equal to one lap.

Akira takes 95 seconds to run one complete lap, so his speed is 1 lap / 95 seconds = 0.010526 laps/second. Since Bob and Akira are running at constant speeds, their speeds are inversely proportional to the time it takes them to reach the easternmost and northernmost points respectively.

Using the same logic, Bob's speed can be calculated as 1 lap / 26 seconds = 0.038462 laps/second. Therefore, Bob takes 1 lap / 0.038462 laps/second = 26 seconds to run one lap of the track.