Expert: Paul Klarreich - 10/22/2006

Question
A airplane is travelling east at 300miles/hr and comes back west at 400miles/hr. Total time it was in the air was 7 hrs. How much distance did it travel (one way)?  

Answer
Questioner:  nihao cai
Category:  Advanced Math
 
Subject:  distance
Question:  A airplane is travelling east at 300miles/hr and comes ALL THE WAY back west at 400miles/hr. Total time it was in the air was 7 hrs. How much distance did it travel (one way)?
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Hi, Nihao,

You must be very careful to state the conditions of the problem.  Was the distance travelled east exactly the same as the distance travelled west?  If the answer is yes, then you really have your problem solved.

Easiest is to write two equations in two variables.  Let:

E = time spent traveling East.
W = time spent traveling West.

Then

300E = distance traveled East.
400W = distance traveled West.

And the following is true:

A. The distances are equal.
B. The total time is 7 hours.

That gives you two equations, since you have two sentences:

300E = 400W
E + W = 7

Write the second as  W = 7 - E and substitute:

300E = 400(7 - E)

300E = 2800 - 400E
700E = 2800
E = 4
W = 3.

Answer: It traveled 1200 miles one way.

Notes:  When you set up verbal problems, make sure that you state EXACTLY what number(s) your variable(s) represent.  If you get lazy and write:  "E = East", you get nowhere and start thinking these are too hard for you.