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Taylor and Jamal are both traveling from the same place, to the same destination. Taylor started traveling on Saturday, and he is traveling 30 miles a day. Jamal didn't start until Sunday, but he is traveling 35 miles a day.

How many days will it take Jamal to catch up to Taylor, and how many miles will they each have traveled?

Answer the questions to solve this problem using a system of equations.

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. (1 point)















2. Write an equation to represent the number of miles Taylor has traveled.

Using x, the number of days Jamal has been traveling, write an expression to represent the number of days Taylor has been traveling. Remember that Taylor started traveling one day before Jamal. Use this expression to write an equation for the number of miles Taylor has traveled. Let y represent the number of miles traveled. (1 point)















3. Write the system of equations using your answers from questions 1 and 2.
(2 points)















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. (2 points)















5. Solve the system of equations. Show your work. (2 points)















6. Interpret your solution. How many days does it take Jamal to catch Taylor? At that time, how many miles have they traveled? (2 points)



Answer :

Answer:

1) y = 35(x - 1)

2) y = 30x

3) y = 30x

y = 35(x - 1)

4) I will substitute for y because both equations are in terms of x.

5) 30x = 35(x - 1)

30x = 35x - 35

5x = 35

x = 7 days

6) It takes Jamal 7 days to catch Taylor. At that time, both Jamal and Taylor will have traveled 30(7) = 210 miles.

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