Question 227740
If a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip?


Step 1.  distance = speed * time


Step 2.  Let t be the time of the trip traveling on time.


Step 3.  Let t-2 be the time if traveling at 55 mph.


Step 4.  Let 55(t-2) be the distance traveling at 55 mph.


Step 5.  Let 35(t+2) be the distance traveling at 35 mph.


Step 6.  Then, 55(t-2)=35(t+2) since the distances are equal in Steps 4 and 5.


Step 7.  Solving the equation in Step 6 yields the following steps


{{{55t-110=35t+70}}}


Add 110-35t to both sides of the equation


{{{55t-110+110-35t=35t+70+110-35t}}}


{{{20t=180}}}


Divide by 20 to both sides of the equation


{{{20t/20=180/20}}}


{{{t=9}}}


Substitute the value of t in Steps 4 or 5.  We'll do both to check if distances are equal


{{{55(9-2)=385}}} miles and {{{35(9+2)=385}}} miles.


Step 8.  The distance is 385 miles.


I hope the above steps were helpful.


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Respectfully,
Dr J

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