Your aunt and uncle took turns driving on a 580-mile trip that took 10 hours. Your uncle drove at a constant speed of 60 mph and your aunt drove a constant speed of 55 mph.

Question

How long did each person drive?

A. Write the two equations. 

B Solve the equations and give both answers.

Answer 1

The formula I made is 60t+55T=580.

I found that t=6 and T=4.

Answer 2

A. First we need to assign variables. We want to know how long each person drove. So, let's say:

A = # hours your aunt drove and U = # hours your uncle drove

Now, when we add up the number of hours they each drove, our total trip time should be 10. So our first equation is:

A + U = 10

Next, we know that the trip total was 580 miles. To find the number of miles driven, we can multiply a person's speed by the number of hours they drove. We know that the number of hours they drove is represented by A and U. When we add up the distances each drove we get our total trip of 580 miles. This gives us the equation:

55A + 60U = 580

These are the two equations we are going to use.

B. Now we can solve our equations using substitution. I am going to solve the first equation for A and then plug that into my second equation:

A + U = 10

-U -U

A = 10 - U

55A + 60U = 580

55(10 - U) + 60U = 580

550 - 55U + 60U = 580

550 + 5U = 580

-550 -550

5U = 30

/5 /5

U = 6

So we now know that your uncle drove 6miles. Now just plug 6 in for U in the first equation and solve for A:

A + U = 10

A + 6 = 10

-6 -6

A = 4

So our uncle drove 6 hours and our aunt drove 4 hours.