<PRE><B>Question 1153492</B>
&lt;br&gt;
Here is an alternative method for solving problems like this that I personally find gets me to the answer faster than the formal algebraic solution suggested by the other tutor.&lt;br&gt;
The distances up and back are the same; the ratio of the two speeds is 2.90:4.90 = 29:49.&lt;br&gt;
That means the fraction of the total time spent going up the mountain was 49/(29+49) = 49/78.&lt;br&gt;
So the number of hours spent going up the mountain was&lt;br&gt;
{{{(49/78)*8 = 392/78 = 196/39}}}&lt;br&gt;
And then the distance up the mountain is rate times time:&lt;br&gt;
{{{(196/39)*2.9}}} = 14.574 miles, to 3 decimal places.&lt;br&gt;
Assuming, then, that &quot;total length of the hike&quot; means both directions, the total length was about 29.15 miles.&lt;br&gt;
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