SOLUTION: In a large marathon, runners start the race in stages. Leanna started in group E and ran at a rate of 3.6 miles per hour. During the race she was passed by Tatiana who ran at a r

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: In a large marathon, runners start the race in stages. Leanna started in group E and ran at a rate of 3.6 miles per hour. During the race she was passed by Tatiana who ran at a r      Log On


   

Question 986169: In a large marathon, runners start the race in stages. Leanna started in group E and ran at a rate of 3.6 miles per hour. During the race she was passed by Tatiana who ran at a rate of 3.9 miles per hour and started in group H, 15 minutes after Leanna started. How far did Leanna run before she was passed by Tatiana?
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the distance Leanna ran after Tatiana started running. Since Leanna had been running for 15 minutes (one-quarter hour) before Tatiana started, she was 3.6 times 0.25 = 0.9 miles ahead.

The amount of time that Tatiana ran until she passed Leanna is the same as the amount of time that Leanna ran starting at her head-start position.

The time that Tatiana ran until she passed Leanna is given by:



The time that Leanna ran after Tatiana started is given by:



Set these two expressions for equal values equal to each other and solve for . Then calculate to get your final answer.

John

My calculator said it, I believe it, that settles it