1. ## Help, please!

Hey, I need some help on this problem.

The trip was only 200 miles, so Bob and Rita rode at 25 mph for a while. Then they doubled their speed for the last part of the trip, so that the total time for the journey would be 5 hours. How far did they drive before they increased their speed?

2. Hallo,
t is the time they traveled at 25 mph.
Than is (5-t) the remaining time.
During this remaining time they travel at a speed of 50 mph.

After 200 miles the journey is completed:

$200=25\cdot \ t+ 50\cdot(5-t)$
$200=25\cdot \ t+ 250-50 \cdot t$
$200=250- 25 \cdot t$
$-50=-25\cdot \ t$
$2= t$

That means: They travel 2 hours at 25 mph: 50 miles
and 3 hours at 50 mph: 150 miles.

Adds up to a total of 200 miles.

3. First set up your equations:

If you are driving so many mph, when you multiply that number by some number of hours, you get the number of miles, so, your first equation should go:

25h1 + 50h2 = 200mi

That is given in the equation. It is also given that we want to make the trip in a total of 5 hours; therefore, the sum of h1 and h2 should be 5:

h1 + h2 =5

That gives us our starting equations.

You can then say that h1 = 5-h2

Then you go back and substitute that into the first equation and solve for h2. Once you get h2, you can easily get h1 by plugging into the second equation.

Make sure that the numbers you get for h1 and h2 sum to your total hours, five.

4. Yeah, earboth's way is probably more efficient.