SOLUTION: You commute to work at a distance of 40 miles and return on the same route at the end of the day. Your average speed on the return trip is 30 miles per hour faster than your avera

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Question 1169053: You commute to work at a distance of 40 miles and return on the same route at the end of the day. Your average speed on the return trip is 30 miles per hour faster than your average speed on the morning’s outgoing trip. If the round trip takes 2 hours, what are your average speeds each way? Define each variable(s).
The equation for this is Time=distance/rate? I could be wrong.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
You commute to work at a distance of 40 miles and return on the same route at the end of the day.
Your average speed on the return trip is 30 miles per hour faster than your average speed on the morning’s outgoing trip.
If the round trip takes 2 hours, what are your average speeds each way? Define each variable(s).
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Let x be the rate commuting to work (in miles per hour).

Then the rate commuting back is (x+30) mph.


The time commuting to work is  40%2Fx  hours.

The time commuting back    is  40%2F%28x%2B30%29  hours.


The total time commuting to work and back is 2 hours, which gives you the "time" equation

    40%2Fx + 40%2F%28x%2B30%29 = 2  hours.    (1)


It is your basic equation.  The setup is just completed.


To solve the equation, multiply both sides by x*(x+30).  You will get


    40*(x+30) + 40x = 2*x*(x+30).


Simplify


    40x + 1200 + 40x = 2x^2 + 60x

    2x^2 - 20x - 1200 = 0

     x^2 - 10x - 600 = 0

Factor left side

    (x-30)*(x+20) = 0.


Of the two roots,  x= 30  and  x= -20, only positive root  x= 30 makes sense.


Hence, the ANSWER is:  the rate commuting to work is 30 mph;  the rate commuting back is 30+30 = 60 mph.



CHECK.  I will check if the equation (1) is valid:  40%2F30 + 40%2F60 = 4%2F3 + 2%2F3 = 2.   ! Correct !

The problem is just solved.

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The method of solution is using the  "time"  equation.

MEMORIZE  this method  (!)