Mr. Smith spent 6 hours hiking along a trail and back. He walked out at the rate of 4 miles per hour and walked back at the rate of 2 miles per hour. How long did it take Mr. Smith to get to the end of the trial?

To get to the end of the trail it would take 2 hours because the walking back hours would be double the walking out rate, but it would still have to equal 6 hours. So walking out would be 2 hours and walking back would be 4 hours which makes the trail 8 miles long.

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dubeyshailja64 dubeyshailja64 · Answer 2 · 2022-01-20T11:16:50+01:00

Linear equations are algebraic equations which represents the value of variables. These equations have unique solutions or sometimes there may be a number of solutions. Linear equation may contain n number of variables.

Given:

[tex]\begin{aligned}\rm\:Total\: time\: taken\: by \:MR. Smith \: &= 6 hours\\\\\rm\:Speed\:while\:going &= 4 \:miles\:per\:hour.\\\\\rm\:Speed \:while\:coming\:back &= 2\: miles\:per \:hour \end[/tex]

Calculations

Let time taken to walk out be [tex]x[/tex] and time taken to walk back be [tex]2x[/tex]. The total time taken will be the summation of [tex]x[/tex] and [tex]2x[/tex] .

[tex]\begin{aligned}\rm\:Total\:time&= 6\:hours\\\\x+2x&= 6\: hours\\\\3x&=6\:hours\end[/tex]

Continuing further,

[tex]x=\dfrac{6}{3}\:hours \\\\x=2\:hours[/tex]

Therefore it can be said that the time taken by Mr. Smith to reach the end of the trial is 2 hours.

It is also observed that the speed while coming back was half of the speed of walking out. So it can be said that the time taken to walk back was twice the time Mr. Smith took to reach the end of the trail.

Learn more about linear equation here:

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