Question 1185319
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First a standard algebraic setup for solving the problem....<br>
d = distance between A and B<br>
time going from A to B: d/45
time going from B to A: d/50<br>
Total driving time: 48-10=38<br>
{{{d/45+d/50=38}}}<br>
Solve using basic algebra; probably start by multiplying both sides by a common denominator to clear fractions.<br>
I leave it to you to finish solving the problem by that method.<br>
Here is a very different way of solving the problem....<br>
The distances both directions are the same; the ratio of speeds is 50:45=10:9.  That means the ratio of times spent at the two speeds is 9:10.<br>
So let the time at 50mph be 9x and the time at 45mph be 10x.<br>
The total time is 38 hours:<br>
{{{9x+10x=38}}}
{{{19x=38}}}
{{{x=2}}}<br>
The time at 50mph is 9x=18 hours; that means the distance between A and B is 50(18)=900 miles.<br>
Note also the time at 45mph is 10x=20 hours, which means the distance between A and B is 45(20)=900 miles -- which of course agrees with the answer we already found.<br>