Question 1071927
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<pre>
Let r" be the actual speed, in mph.

Then the hypothetical speed is (r+13) mph.


Moving at the speed of "r" miles per hour, the car spends {{{1950/r}}} hours.

Traveling with the hypothetical speed, the car would spend {{{1950/(r+13)}}} hours.

The condition says

{{{1950/r - 1950/(r+13)}}} = 5.


It is your "time" equation.  You must solve it for "r". 
To do it, multiply both sides by the common denominator r*(r+13). You will get

1950*(r+13) - 1950*r = 5r*(r+13),

{{{1950*13}}} = {{{5r^2 + 5*13*r}}},

{{{r^2 + 13r - 5070}}} = 0.

Factor it:

(r+78)*(r-65) = 0.


The only positive root is r = 65.
</pre>

<U>Answer</U>. The speed of the car is 65 mph.