SOLUTION: The president of a company traveled 1600 mi by jet and 300 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 10 h. Find the ra

Algebra ->  Equations -> SOLUTION: The president of a company traveled 1600 mi by jet and 300 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 10 h. Find the ra      Log On


   

Question 1173836: The president of a company traveled 1600 mi by jet and 300 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 10 h. Find the rate of the jet.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

x = rate of the prop plane;

4x = rate of the jet.


The time equation is


    1600%2F%284x%29 + 300%2Fx = 10  hours.


Simplify

    400%2Fx + 300%2Fx = 10

    700%2Fx = 10


       x   = 700%2F10 = 70 miles per hour  is the rate of the prop plane.

Hence, the rate of the jet is  4*70 = 280 mph.


CHECK.  1600%2F280 + 300%2F70 = 40%2F7 + 30%2F7 = 70%2F7 = 10 hours.   ! Correct !

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor provided a good formal algebraic solution to the problem.

If formal algebra is not required, note that a quick informal solution can be obtained by using logical reasoning and some simple mental arithmetic.

Since the rate of the jet is 4 times the rate of the prop plane, 1600 miles by jet is equivalent to 400 miles in the prop plane.
That makes the trip equivalent to 700 miles on the prop plane in 10 hours.
That makes the speed of the prop plane 700/10 = 70mph; and then the speed of the jet is 4 times that, or 280mph.

ANSWER: 280 mph for the jet.