Two planes left the same airport traveling in opposite directions. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes were 1825 miles apart. The second plane left at 10:00 a.m. and its average rate was 108 miles per hour slower than the first plane's average rate. Let x represent the first plane's average rate.

Question

Two planes left the same airport traveling in opposite directions. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes were 1825 miles apart. The second plane left at 10:00 a.m. and its average rate was 108 miles per hour slower than the first plane's average rate. Let x represent the first plane's average rate.

What was the first plane's average rate?

Enter an equation that can be used to solve this problem in the first box.

Solve for x and enter the first plane's average rate in the second box.

Answer 1

Let x represent the first plane's average rate.

The first plane traveled for 2.25 hours longer than the second plane, which means the second plane traveled for 2.25 hours less than the first plane.

Since the distance traveled is equal to rate multiplied by time, the distance traveled by the first plane is x*(2.25+x) and the distance traveled by the second plane is (x-108)*2.25.

The sum of the distances traveled by both planes is equal to 1825 miles, so:

x*(2.25+x) + (x-108)*2.25 = 1825

Now, solve for x to find the first plane's average rate.