Reply to Joe Mendez:
Great work on solving the equation and providing a clear step-by-step breakdown! Here’s a similar example for us to work through together.
Example:
Solve the equation: A car travels a total distance of 240 miles. If the car travels at a constant speed of 60 miles per hour for some hours, and then at 40 miles per hour for the rest of the journey, how long did the car travel at 40 miles per hour if the entire trip took 4 hours?
Let \( x \) be the time (in hours) traveled at 40 miles per hour. The time traveled at 60 miles per hour will then be \( 4 - x \).
The distance traveled at 60 miles per hour is given by the formula:
Distance = Speed × Time
So, the distance is:
\( \text{Distance at 60 mph} = 60 \times (4 - x) \)
The distance traveled at 40 miles per hour is:
\( \text{Distance at 40 mph} = 40 \times x \)
Since the total distance is 240 miles, we can set up the equation:
\[ 60(4 - x) + 40x = 240 \]
Now, let's solve for \( x \):
-
Distribute the 60:
\( 240 - 60x + 40x = 240 \) -
Combine like terms:
\( 240 - 20x = 240 \) -
Subtract 240 from both sides:
\( -20x = 0 \) -
Divide by -20:
\( x = 0 \)
So, the car did not travel at 40 miles per hour at all during the trip; it traveled the entire distance at 60 miles per hour.
Feel free to reach out if you have any more questions or need further clarification!
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