Question 1085092
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Let "t" be the average speed of the truck, in mph.

Then the average speed of the car is (t+10) mph.


Then your "total combined time equation" is

{{{378/t + 320/(t+10)}}} = 12.


Indeed, {{{378/t}}} is the time for the truck to cover 378 miles, while {{{320/(t+10)}}}  is the time for the car to cover 320 miles.


To solve the equation, multiply both sides by t*(t+10). You will get

378*(t+10) + 320t = 12t*(t+10).


Simplify and solve this quadratic equation by any method you know.


<U>Answer</U>.  The average speed of the truck is 54 mph.  The average speed of the car is 64 mph.


<U>Check</U>.   {{{378/54}}} + {{{320/64}}} = 7 + 5 = 12.  Correct !!
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