Question

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take graham and max to meet at the same altitude?

Answer 1

Graham: -50x + 14,040

Max:  20x + 12,500

   Graham      =        Max

-50x + 14,040 = 20x + 12,500

+50x                 +50x              

            14,040 = 70x + 12,500

         -12,500             -12.500

             1,540  = 70x

              $\frac{1,540}{70} = \frac{70x}{70}$

                220 = x

Answer: 220 minutes (3 hours 40 minutes)

Answer 2

Answer:

22 minutes

Step-by-step explanation:

Graham is hiking at an attitude of 14,040 feet, and descending 50 feet each minute.

Let the time when graham and max meet at same point be x minutes.

As, Graham is descending 50 feet each minute, so the position of Graham after x minutes is given by the expression

$14040-50x$

Now, Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute.

As, Max is ascending 20 feet each minute, so the position of Max after x minutes is given by the expression

$12500+20x$

Now, to get the value of x we need to equate the two expressions.

$14040-50x=12500+20x$

$\implies 70x=14040-12500$

$\implies 70x=1540$

$\implies x=\frac{1540}{70}$

$\implies x=22$

Hence, it will take 22 minutes for Graham and Max to meet at the same altitude.