need help solving

Question

 On a road trip with a friend, you drive about 70 miles per hour, and your friend drives about 60 miles per hour. The plan is to drive less than 15 hours and at least 600 miles each day. Your friend will drive more hours than you. How many hours can you and your friend each drive in 1 day?

1. 
   

Answer 1

It's best to solve as a linear programming problem.

X and Y are the driving times in HOURS

X+Y <= 15 <--- no more than 15 hours;

60x + 70y >= 600 <-- at least 600 miles

X<Y <--- faster driver must driver more time

The critical point that maximizes the mileage is at (7.5,7.5)

So x<7.5 ---> 7.5 < y < 15 and 0 < x < 7.5