speed of trip

Question

a marine platoon went on a 20 mile hike that took 6 hours to complete.  for the first 12 miles the platoon hiked at a constant speed.  For the last 8 miles the platoon increased its speed by 1 mile per hour.  find the speed of the platoon on the last

Answer 1

Remember that rate * time = distance and therefore time = distance /rate

 

The time for the entire trip is 6 hours.  Let x be the rate for the first 12 miles.

 

The time for the first 12 miles is 12/x and for the last 8 miles is 8/(x+1)

Therefore, (12/x) + [8/(x+1)] = 6

Divide by 2 and add the fractions over a common denominator:

(10x + 6)/[x(x+1)] = 3

Clear fractions and collect terms:

3x² - 7x - 6 = 0 = (3x + 2)(x -3).

 

The negative root makes no physical sense, but x = 3 does.