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)10h = 8h + 3 (B)10 = 3h + 8 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)10h = 8h + 3 (B)10 = 3h + 8  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 faster than Krysta. We want to find out when Erin will catch up to Krysta. To do this, we need to set up an equation that represents the distance each person has traveled after h hours. Since distance equals rate times time, Erin's distance can be represented as 10h (because she bikes at 10 miles per hour), and Krysta's distance can be represented as 8h + 3 (because she starts 3 miles ahead and bikes at 8 miles per hour). We set these equal to each other to find when the distances are the same, which means Erin has caught up to Krysta.Write Equation: Now we write the equation based on the above reasoning. The correct equation is: 10h = 8h + 3 This equation represents the point in time when Erin has traveled the same distance as Krysta, meaning Erin has caught up.Isolate Variable: To solve for h, we need to isolate the variable on one side of the equation. We can do this by subtracting 8h from both sides of the equation: 10h - 8h = 8h + 3 - 8h This simplifies to: 2h = 3Solve for h: Now we divide both sides of the equation by 2 to solve for h: 2h / 2 = 3 / 2 This gives us: h = 3/2Convert to Time: We convert the fraction to a mixed number or decimal to make it easier to understand in the context of time. Since there are 60 minutes in an hour, half an hour is 30 minutes. Therefore, 3/2 hours is the same as 1 hour and 30 minutes.

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