Word problem for Algebra 1 need equation and answer

Question

Michael and Kevin are running.  Kevin gets a three mile head start and runs a rate of 5.5 mph.  Michael runs a rate of 7 mph.  How many hours will it take Michael to catch up to Kevin?

Answer 1

Hi Emily, I like to set up a table for problems like this. Here is the table:

 

Runner       Distance       Rate        Time

---------------------------------------------

Kevin           d - 3            5.5          t

 

Michael           d               7            t

 

d represents the distance Michael will run. Since Kevin gets a 3 mile head start, he will run d - 3 miles.

 

t represent the time each runner will run.

 

Using the formula, D(istance) = R(ate) * T(ime), we can set up an equation representing both runners. Keep in mind, t will be the same for both runners.

 

Equation for Kevin:

 

d - 3 = 5.5 * t

 

Equation for Michael:

 

d = 7 * t

 

Since t is the same for both runners, solve both equations for t:

 

For Kevin, t = (d - 3) / 5.5

 

For Michael, t = d / 7

 

Then, (d - 3) / 5.5 = d / 7, remember t will be the same for both runners.

 

Cross multiply and solve for d:

 

7 * (d - 3) = 5.5 * d

 

7d - 21 = 5.5 * d

 

Subtract 5.5 * d from both sides:

 

1.5 * d - 21 = 0

 

Add 21 to both sides:

 

1.5 * d = 21

 

Divide both sides by 1.5:

 

d = 14

 

The distance Michael will run to catch Kevin is 14 miles.

 

Using the distance equation for Michael, we can find how long it takes for Michael to run 14 miles:

 

d = 7 * t

 

14 = 7 * t

 

Divide both sides by 7:

 

t = 2

 

It will take Michael 2 hours to catch Kevin.

 

Check:

 

Using the distance formula for Kevin:

 

d -3 = 5.5 * t

 

14 - 3 = 5.5 * t

 

11 = 5.5 * t

 

Divide both sides by 5.5:

 

t = 2

 

This shows Kevin will run for 2 hours before Michael catches him.

 

Questions?