SOLUTION: how do i solve this problem algebraically? two airplanes left the same airport traveling in opposite directions. if one airplane averages 400 mph and the other 250 mph, how many

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Question 290191: how do i solve this problem algebraically?
two airplanes left the same airport traveling in opposite directions. if one airplane averages 400 mph and the other 250 mph, how many hours willl it take for the distance between them be 1625 miles?
i know the answer is 2.5 hours but i dont know how to get there.
Found 2 solutions by solver91311, rentot12:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

If the two vehicles are traveling in opposite directions, then the distance each travels adds to the distance between them. Using the fact that distance equals rate times time, and at any given time, both will have traveled the same amount of time, we can say that the faster plane traveled

miles

and the slower plane traveled

miles

and the sum of these two distances is

Just solve for

John

Answer by rentot12(1) (Show Source):
You can put this solution on YOUR website!
First, make a table for the given terms:

Let's say airplane A is the one that flies for 400mph and airplane B that flies for 250mph. Since what we are looking for is "how many hours", the column for Time for both A & B will be left unknown and it was because there was no time given on either of the two airplanes. The unknown time will be represented by (t).
Remember these formulas back from your physics (don't worry about physics stuff on this algebra matter. just recall these formulas to help you solve with this kind of question):

Distance = rate x time

v = s/t v = stands for velocity or rate ; s = stands for speed or distance

s = vt
_______________________________________________________________________________
Airplane | Rate | Time | Distance (rate x time)
________________________________________________________________________________
A | 400mph | t | 400(t)
________________________________________________________________________________
B | 250mph | t | 250(t)
________________________________________________________________________________
Total | 1625 miles
________________________________________________________________________________

Remember to create a table for this kind of question so we could easily identify which is which and accord it to a linear equation.

Then, apply linear equation.

400(t) + 250(t) = 1625 miles
650t = 1625

650t = 1625
____ _____
650 650

t = 2.5 --------> your answer match.
so let's check

checking:
just substitute the (t)

400(2.5) + 250(2.5) = 1625

1000 + 625 = 1625

1625 = 1625 ----> correct!

I hope this helps. This is the first question here that i answered. Goodluck!