Please help me with this problem.
Two cars started from the same point and traveled on a straight course in
opposite directions for exactly 2 hours, at which time they were 208 miles
apart. If one car traveled, on average, 8 miles per hour faster than the other
car, what was the average speed for each car for the 2-hour trip?
Thank you.
Never mind. I figured it out. :)
But now I am stuck with this one. Please help!
A group can charter a particular aircraft at a fixed total cost. If 36 people
charter the aircraft rather than 40 people, then the cost per person is greater by
$12. What is the cost per person if 40 people charter the aircraft?
Thanks.
How about simply...
40x = 36(x+12)
To solve this problem, we can set up a system of equations.
Let's say the average speed of one car is x miles per hour. Since the other car is traveling 8 miles per hour faster, its average speed is (x + 8) miles per hour.
We know that the total travel time for both cars is 2 hours, and the total distance between them is 208 miles.
The distance traveled by the first car is speed multiplied by time, which is equal to x * 2 = 2x miles.
Similarly, the distance traveled by the second car is (x + 8) * 2 = 2(x + 8) miles.
Since they are traveling in opposite directions, the sum of their distances will give us the total distance between them: 2x + 2(x + 8) = 208.
Now, we can solve this equation to find the value of x, which will give us the average speed of the first car:
2x + 2(x + 8) = 208
2x + 2x + 16 = 208
4x + 16 = 208
4x = 192
x = 48
So, the average speed of the first car is 48 miles per hour, and the average speed of the second car (which is 8 miles per hour faster) is 48 + 8 = 56 miles per hour.
Therefore, the average speed for each car for the 2-hour trip is 48 miles per hour and 56 miles per hour, respectively.