Question

Taylor and Jamal are both traveling from the same place, to the same destination. Taylor are traveling on Saturday, and he is traveling 30 miles a day. Jamal didn’t start until Sunday, but he’s traveling 35 miles a day. How many days will it take Jamal to catch up to taylor, and how many miles will they each other traveled?

1. Write an equation to represent the number of miles Jamal has traveled. Use x to
represent the number of days Jamal has been traveling and y to represent the number of miles he has traveled.

2. Using X, the number of days Jamal has been traveling, write expression to represent the number of days taylor has been traveling. Remember that Taylor started traveling one day before Jamal. Uses expression to write an equation for the number of miles taylor has been traveled. Let Y represent the number of miles traveled.

3. write the system of equations using your answers from question one and two.

4. You will use substitution to solve this system. Which variable will you substitute for and why? Show the equation that results from the substitution

5. Solve the system of equations show your work.

6. Interpret your solution. How many days does it take for Jamal to catch up to taylor? at the time How many miles have they traveled?

Answer 1

1. The equation to represent the number of miles Jamal has traveled is y = 35x

2. The equation for the number of miles Taylor has traveled is Y = 30(x + 1).

3. The system of equations can be written as:

y = 35x

Y = 30(x + 1)

4. Substituting Y = 30(x + 1) into y = 35x, we get:

35x = 30(x + 1)

5. Now, we can solve the system of equations:

35x = 30x + 30 and y=35x

x = 6, y = 210

6.The solution shows that Jamal will catch up to Taylor in 6 days, and at that time, they will have both traveled 210 miles.

1. The equation to represent the number of miles Jamal has traveled is y = 35x, where x represents the number of days Jamal has been traveling and y represents the number of miles he has traveled. This equation shows that the number of miles Jamal has traveled is directly proportional to the number of days he has been traveling, with a constant rate of 35 miles per day.

2. Since Taylor started traveling one day before Jamal, the expression to represent the number of days Taylor has been traveling is x + 1. Since Taylor is traveling 30 miles a day, the equation for the number of miles Taylor has traveled is Y = 30(x + 1), where Y represents the number of miles traveled.

3. The system of equations can be written as:

y = 35x

Y = 30(x + 1)

4. To solve this system using substitution, we will substitute the expression for Y from equation 2 into equation 1. This is because we want to find the point where their distances are equal, so we substitute the equation that represents the number of miles Taylor has traveled into the equation for Jamal's miles traveled.

Substituting Y = 30(x + 1) into y = 35x, we get:

35x = 30(x + 1)

5. Now, we can solve the system of equations:

35x = 30x + 30 (Distribute 30)

35x - 30x = 30 (Subtract 30x from both sides)

5x = 30 (Combine like terms)

x = 6 (Divide both sides by 5)

To find the number of miles traveled, substitute the value of x into either equation:

y = 35x

y = 35 * 6

y = 210

So, it will take Jamal 6 days to catch up to Taylor, and at that time, they will have traveled 210 miles.

6. The solution shows that Jamal will catch up to Taylor in 6 days, and at that time, they will have both traveled 210 miles. This means that Jamal's faster pace allows him to catch up to Taylor even though he started one day later.