Question 1093155
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Let D be the distance between cities, in miles.

Then Victor traveled this distance in {{{D/34}}} hours at the speed 34 mph.

Had he moved at the speed 48 mph, he would cover this distance in {{{D/48}}} hours.


The condition says that the difference  {{{D/34}}} - {{{D/48}}} is 7 hours.


It gives you an equation

{{{D/34}}} - {{{D/48}}}  = 7.


To solve it, multiply both sides by 34*48. You will get

48D - 34D = 7*34*48,   or


14D = 7*34*48  ====>  D = {{{(7*34*48)/14}}} = 34*24 = 816 miles.


<U>Answer</U>.  The distance between cities is 816 miles.
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Solved.