Mary Thon starts at a point of 26 miles FROM school and runs TOWARD the school at a rate of 6 Miles per hour. (mph) Randy Miles starts FROM school 1.3 hours later and runs TOWARD MARY at a rate of 8 mph.
x= number of hours that mary has been running
Question-------------------------------
A) in terms of X how many hours has randy been running
B) how far away is he from the school?
C) How lang have mary AND randy been running before they meet?
D)How far FROM SCHOOL do they meet?
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sorry that its so long, but if you could help me i would really appreatiate it.
Thank you.
A) X - 1.3
B) 8 (X-1.3)
C) They meet when distances from school are equal
26 - 6X = 8 (X-1.3)
Solve for X when they meet. Call it X'
D) After you solve for X', use
Distance = 26 - 6X'
thank you so much!
No problem! I can help you with that. Let's break it down step-by-step:
Given information:
- Mary Thon starts 26 miles away from school and runs toward the school at a rate of 6 mph.
- Randy Miles starts from school 1.3 hours later and runs toward Mary at a rate of 8 mph.
Step 1: Determine how long Mary has been running (x):
- Mary's running speed is given as 6 mph.
- Mary's initial distance from school is 26 miles.
- Mary's formula to determine the time she has been running is: distance = rate * time.
- Therefore, 26 = 6 * x.
- Solve the equation for x: x = 26/6.
- Simplifying, x ≈ 4.33 hours.
Answer A: Randy has been running for x - 1.3 hours.
- Since Randy starts 1.3 hours later than Mary, his running time will be x minus 1.3.
- Randy's running time is approximately 4.33 - 1.3 = 3.03 hours.
Answer B: Determine Randy's distance from the school after running for x - 1.3 hours.
- Randy's running speed is given as 8 mph.
- Randy's formula to determine the distance from the school is: distance = rate * time.
- Therefore, Randy's distance from the school is: distance = 8 * (x - 1.3).
- Simplifying, distance = 8 * (4.33 - 1.3).
- Therefore, Randy is approximately 21.04 miles away from the school.
Answer C: Determine the total running time for both Mary and Randy before they meet.
- Mary runs for x hours, and Randy runs for x - 1.3 hours.
- The total running time is x + (x - 1.3).
- Simplifying, the total running time is approximately 4.33 + 3.03 = 7.36 hours.
Answer D: Determine the distance from the school where they meet.
- Mary's distance from the school after running for x hours is 0 miles (since she reaches the school).
- Randy's distance from the school after running for x - 1.3 hours is approximately 21.04 miles.
- Therefore, they meet 21.04 miles from the school.
I hope this helps! Let me know if you have any further questions.
No problem! Let's break down the problem step by step and solve it together.
We know that Mary starts 26 miles away from the school and runs towards the school at a rate of 6 mph. We'll use the formula distance = rate × time to find out how far Mary has run in terms of x.
A) In terms of x, we'll use the formula distance = rate × time. Mary's rate is 6 mph, and she has been running for x hours. So, the distance Mary has run is 6x miles.
Now let's move on to Randy. Randy starts from the school 1.3 hours later and runs toward Mary at a rate of 8 mph.
B) We want to find how far away Randy is from the school. Since Randy starts from the school, we know his initial distance is 0 miles. He has been running for x - 1.3 hours (because he starts 1.3 hours later than Mary). So, the distance Randy has run is 8(x - 1.3) miles.
C) To find out how long both Mary and Randy have been running before they meet, we need to set their distances equal to each other. Mary's distance is 6x miles, and Randy's distance is 8(x - 1.3) miles. So, we can write the equation 6x = 8(x - 1.3).
D) To find how far from the school they meet, we need to substitute the value of x into either Mary's or Randy's distance formula. Let's use Mary's distance formula. When they meet, the distance Mary has run is the same distance from the school as Randy. So, the distance from the school where they meet is equal to the distance Mary has run, which is 6x miles.
Now, with the equations we found:
A) In terms of x, Randy has been running for x - 1.3 hours.
B) Randy is x miles away from the school.
C) Mary and Randy have been running for x hours before they meet.
D) They meet x miles away from the school.
To solve for x and find the exact values, we need to solve the equation 6x = 8(x - 1.3). You can solve it by distributing and collecting like terms and then solving for x.