The Coleman family is moving to a new home on the other side of the state. Lucy Coleman leaves first, hauling a trailer and traveling at a constant speed of 55 miles per hour. When her husband, Tristan, leaves in his car, Lucy is already 10 miles away. Tristan drives at a constant speed of 60 miles per hour. Which equation can you use to find h, the number of hours it will take for Tristan to catch up to Lucy? Choices: (A)10 + 55h = 60h (B)55 + 10h = 60h How long will it take for Tristan to catch up to Lucy? Simplify any fractions. ____ hours

Question

The Coleman family is moving to a new home on the other side of the state. Lucy Coleman leaves first, hauling a trailer and traveling at a constant speed of 55 miles per hour. When her husband, Tristan, leaves in his car, Lucy is already 10 miles away. Tristan drives at a constant speed of 60 miles per hour. Which equation can you use to find h, the number of hours it will take for Tristan to catch up to Lucy?   Choices: (A)10 + 55h = 60h (B)55 + 10h = 60h  How long will it take for Tristan to catch up to Lucy? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Up Equation: Let's first set up the equation to find h, the number of hours it will take for Tristan to catch up to Lucy. We know that Lucy has a 10-mile head start and is traveling at 55 miles per hour. Tristan is traveling at 60 miles per hour. We want to find the point where the distance Tristan has traveled equals the distance Lucy has traveled plus her 10-mile head start.  The distance that Lucy travels can be represented as 55h (since distance = speed × time), and the distance that Tristan travels can be represented as 60h. To account for Lucy's head start, we add 10 miles to her distance. Therefore, the equation that represents the situation is:  10 + 55h = 60h  This is choice (A).Find h: Now we need to solve the equation for h.  10 + 55h = 60h  Subtract 55h from both sides to isolate the variable h on one side of the equation:  10 + 55h - 55h = 60h - 55h 10 = 5h  Now, divide both sides by 5 to solve for h:  10 / 5 = 5h / 5 2 = h  So, it will take Tristan 2 hours to catch up to Lucy.

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