SOLUTION: Please help me solve this equation: You commute 56 miles one way to work. The trip to work takes 10 minutes longer than the trip to home. Your average speed on the trip home is

Question 173044: Please help me solve this equation:
You commute 56 miles one way to work. The trip to work takes 10 minutes longer than the trip to home. Your average speed on the trip home is 8 miles per hour faster. What is your average speed on the trip home?

thank you!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: 10 minutes = 1/6 of an hour

Since the distance of the commute is 56 miles, this means that

Going to Work:

Since "The trip to work takes 10 minutes longer than the trip to home", this means that the time is (in minutes) or (in hours)

We'll use the expression

Start with the distance rate time formula

Plug in and replace "t" with

Combine and to get

Divide both sides by to isolate "r"

Multiply 56 by the reciprocal of .

Multiply 56 and 6 to get 336

So after isolating "r", we get

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

Coming Home:

Now because the "average speed on the trip home is 8 miles per hour faster", this means that the new rate is

Go back to the distance rate time formula

Plug in (the commute distance hasn't changed) and replace "r" with (since the speed is 8 mph greater)

Plug in

Distribute

Multiply EVERY term by the LCD to clear the fractions.

Distribute

Subtract 336t from both sides. Subtract 56 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for t

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible time values (coming home) are or

However a negative time does NOT make sense. So the only answer is

So the time to commute home is 1 hour.

Note: This means that the time to get to work is 1 hour and 10 minutes (or 70 minutes)

Go back to the distance rate time formula

Plug in and (which is the time coming home)

Multiply

=====================================================

Answer:

So the solution is

This means that the average speed coming home is 56 miles per hour.

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