Last Saturday, Erin and Krysta each biked the Prairie Point Trail, a 20-mile path leading to the peak of Prairie Point Mountain. Both girls started at 7:00 A.M., heading toward the peak. Erin started at the trailhead and biked at a constant speed of 10 miles per hour. Krysta started at an entry point 3 miles ahead of the trailhead and rode at a steady pace of 8 miles per hour. If each girl kept a constant speed, which equation can you use to find h, the number of hours it took for Erin to catch up to Krysta? Choices: (A)10 = 3h + 8 (B)10h = 8h + 3 How long did it take for Erin to catch up to Krysta? Simplify any fractions. ____ hours

Question

Last Saturday, Erin and Krysta each biked the Prairie Point Trail, a 20-mile path leading to the peak of Prairie Point Mountain. Both girls started at 7:00 A.M., heading toward the peak. Erin started at the trailhead and biked at a constant speed of 10 miles per hour. Krysta started at an entry point 3 miles ahead of the trailhead and rode at a steady pace of 8 miles per hour. If each girl kept a constant speed, which equation can you use to find h, the number of hours it took for Erin to catch up to Krysta?   Choices: (A)10 = 3h + 8 (B)10h = 8h + 3  How long did it take for Erin to catch up to Krysta? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Up Problem: Let's set up the problem. Erin starts 3 miles behind Krysta and is biking at a faster speed. We want to find out when the distance Erin has biked equals the distance Krysta has biked. Since Krysta has a 3-mile head start, we need to add this to the distance she travels at her speed of 8 miles per hour. Erin's distance will be her speed (10 miles per hour) times the number of hours, h. The equation will set these two expressions equal to each other to find when Erin catches up to Krysta.Write Equation for Erin: We can write the equation for the distance Erin travels as 10h, since she travels at 10 miles per hour for h hours. For Krysta, we add her head start of 3 miles to the distance she travels at 8 miles per hour for h hours, which gives us 8h + 3. Setting these equal to each other gives us the equation 10h = 8h + 3.Solve Equation for h: Now we solve the equation 10h = 8h + 3 for h. We subtract 8h from both sides to isolate the variable h on one side of the equation. 10h - 8h = 8h + 3 - 8h This simplifies to: 2h = 3Find Value of h: To find the value of h, we divide both sides of the equation by 2. 2h / 2 = 3 / 2 This gives us: h = 3 / 2Calculate Time Taken: We simplify the fraction 3 / 2 to get the number of hours it took Erin to catch up to Krysta. 3 / 2 = 1.5 So, it took Erin 1.5 hours to catch up to Krysta.

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