Algebra homework help

Question

Two trains leave a train station at the same time. One travels east at 10 miles per hour. The other train travels west at 8 miles per hour. In how many hours will the two trains be 153 miles apart?

Solve the problem.

A loan officer at a bank has $100,000 to lend and is required to obtain an average return of  per year. If he can lend at the rate of  or the rate of  how much can he lend at the  rate and still meet his required return?

Find a and b.

If 0 < 2x < 6, then a < x² < b.

Answer 1

153/(10+8) = 8.5 hours

they will be 153 miles apart in 8 1/2 hours

.14x + .11(100,000-x)= .13(100,000)

.14x -.11x = 13,000-11,000 = 2000

.03x = 2000

x=2000/.03= 200,000/3 = 66,666.67 invested at 14%

100000-x = 33,333.33 dollars invested at 11%

11 is within 2 of 13

14 is within 1 of 13

twice as much is invested at 14%

2/1 = 66666.67/33333.33

0<2x<6

0<x <3

0<x^2<9

a=0, b= 9