Dionne is running clockwise. She can run around a circular track in 120 seconds. Basha, running counter-clockwise, meets Dionne every 48 seconds. Sandra runs clockwise and passes Basha every 240 seconds. How often does Sandra meet Dionne in 10 minutes?
Let Tb be the one-lap time for Basha.
The frequency that Basha and Dionne encounter is
1/48 = 1/120 + 1/Tb, so
1/Tb = 10/480 - 4/480 = 6/480 = 1/80
Tb = 80 seconds
With Sandra and Basha running in opposite directions, and Basha running so fast, they would have to meet more often than every 240 seonds. I believe you made and error stating that Sandra runs clockwise, opposeite to Basha. Check the wording of the problem again.
To find out how often Sandra meets Dionne in 10 minutes, we need to first determine their individual speeds and how long it takes them to complete one lap around the circular track.
Let's start by finding Dionne's speed. We are given that Dionne can run around the track in 120 seconds. Therefore, in one second, Dionne covers 1/120th of the track.
Next, let's determine Basha's speed. We are given that Basha meets Dionne every 48 seconds. This means that Basha runs a distance equal to Dionne's lap length in 48 seconds. Thus, Basha's speed is 1/48th of the track per second.
Now, let's find Sandra's speed. We are told that Sandra passes Basha every 240 seconds, which means that Sandra runs a distance equal to Basha's lap length in 240 seconds. Therefore, Sandra's speed is 1/240th of the track per second.
Now that we have their individual speeds, we can determine how often Sandra meets Dionne in 10 minutes.
Since 10 minutes is equal to 10 * 60 = 600 seconds, we need to find the number of times Sandra meets Dionne within this time period.
First, we calculate how long it takes for Dionne and Sandra to meet. Since they are both running clockwise, they meet at a combined rate of Dionne's speed + Sandra's speed per second. So, the time it takes them to meet is given by:
1 / (1/120 + 1/240) = 1 / (1/120 + 1/240) = 80 seconds.
Since Dionne and Sandra meet every 80 seconds, we divide the total time (600 seconds) by 80 seconds to find out how many times they meet:
600 seconds / 80 seconds = 7.5 times.
Therefore, Sandra meets Dionne 7 times in 10 minutes.