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Answer :
To find out the distance the first runner travels when the two runners meet on the circular track, we can break down the problem into several simple steps:
1. Understand the Total Circumference: The track is circular, with a circumference of 140 meters. This means the total distance around the track is 140 meters.
2. Determine Speeds:
- The first runner has a speed of 4 meters per minute (m/m).
- The second runner has a speed of 6 meters per minute (m/m).
3. Calculate the Relative Speed: Since the runners are moving toward each other, you can add their speeds to find the relative speed at which the distance between them is closing.
[tex]\[
\text{Relative Speed} = 4 \, \text{m/m} + 6 \, \text{m/m} = 10 \, \text{meters per minute}
\][/tex]
4. Find the Time to Meet: The time it takes for them to meet is the time it takes for their combined relative speed to cover the entire circumference of the track.
[tex]\[
\text{Time to Meet} = \frac{\text{Circumference}}{\text{Relative Speed}} = \frac{140 \, \text{meters}}{10 \, \text{meters per minute}} = 14 \, \text{minutes}
\][/tex]
5. Calculate the Distance Traveled by the First Runner: Now that we know it takes 14 minutes for the runners to meet, we can determine how far the first runner has traveled in that time.
[tex]\[
\text{Distance Traveled by First Runner} = \text{Speed of First Runner} \times \text{Time to Meet} = 4 \, \text{m/m} \times 14 \, \text{minutes} = 56 \, \text{meters}
\][/tex]
Therefore, when the runners meet, the first runner has traveled 56 meters.
1. Understand the Total Circumference: The track is circular, with a circumference of 140 meters. This means the total distance around the track is 140 meters.
2. Determine Speeds:
- The first runner has a speed of 4 meters per minute (m/m).
- The second runner has a speed of 6 meters per minute (m/m).
3. Calculate the Relative Speed: Since the runners are moving toward each other, you can add their speeds to find the relative speed at which the distance between them is closing.
[tex]\[
\text{Relative Speed} = 4 \, \text{m/m} + 6 \, \text{m/m} = 10 \, \text{meters per minute}
\][/tex]
4. Find the Time to Meet: The time it takes for them to meet is the time it takes for their combined relative speed to cover the entire circumference of the track.
[tex]\[
\text{Time to Meet} = \frac{\text{Circumference}}{\text{Relative Speed}} = \frac{140 \, \text{meters}}{10 \, \text{meters per minute}} = 14 \, \text{minutes}
\][/tex]
5. Calculate the Distance Traveled by the First Runner: Now that we know it takes 14 minutes for the runners to meet, we can determine how far the first runner has traveled in that time.
[tex]\[
\text{Distance Traveled by First Runner} = \text{Speed of First Runner} \times \text{Time to Meet} = 4 \, \text{m/m} \times 14 \, \text{minutes} = 56 \, \text{meters}
\][/tex]
Therefore, when the runners meet, the first runner has traveled 56 meters.
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