Question

The temperature at the base of a mountain is 9 degrees. For every 1000 feet rise in altitude, the temperature drops 3 degrees. The hikers want to go back down before the temperature reaches -6degrees. At what altitude should the hikers turn back

Answer 1

5000 feet

Explanation:

We can solve this question by using arithmetic series concept.

Now, difference of temperature is key point here. Initial temperate is 9 degrees. Final temperature where hiker wants to turn back is -6 degree.

For every 1000 feet there is drop of 3 degree. from this data we can calculate the returning point altitude.

Now For arithmetic sequence, formula is

T(n) = a + (n-1)d

where T(n) is final term which is -6

a is initial term which is 9

d is common difference which is -3. Note that common difference is taken in negative because temperature is decreasing at every 1000 feet.

Now by putting values

-6 = 9 + (n-1)*(-3)

-6-9 = (n-1)*(-3)

-15 = -3n+3

-18 = -3n

so, n = 6

Now remember that every 1000 feet there is drop of temperature, and temperature dropped first time after hiker covered 1000 feet, so we have to eliminate first term here, which means we have to take (n-1) here to calculate the total altitude

So, we have to multiply the value of n with 1000 to calculate original altitude.

Altitude = 1000*(n-1)

Altitude = (1000)(5)

Altitude = 5000 feet.