SOLUTION: 1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-four

Algebra ->  Equations -> SOLUTION: 1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-four      Log On


   

Question 391955: 1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and ship.
2. A person invested $10,000. The greater part is invested at 6% and the remainder at 5%. The annual income from the greater part is $160 more than the annual income from the smaller part. What is the smaller part of investment?
3. What amount of mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of mixture which is 45% alcohol? What equation will express this problem?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and ship.
:
Let x = speed of plane
and
Let y = speed of ship
:
Two distance equations; dist = time * speed
:
4x + 25y = 1580
and
4(.5x) + 25(1.25y) = 1315
2x + 31.25y = 1315
:
Multiply above equation by 2. Subtract the first equation
4x + 62.5y = 2630
4x + 25y = 1580
---------------------subtraction eliminates x, find y:
37.5y = 1050
y = 1050%2F37.5
y = 28 mph speed of the ship
:
Find x using the 1st equation
4x + 25(28) = 1580
4x + 700 = 1580
4x = 1580 - 700
4x = 880
x = 880%2F4
x = 220 mph speed of the plane
:
Check solution in 2nd equation:
4(110) + 25(35) =
440 + 875 = 1315
:
:
2. A person invested $10,000. The greater part is invested at 6% and the remainder at 5% The annual income from the greater part is $160 more than the
annual income from the smaller part.
What is the smaller part of investment?
:
Let x = the smaller part of the investment
then
(10000-x) = the larger part
:
.06(10000-x) - .05x = 160
:
:
3. What amount of mixture, one 95% alcohol and the other 15% alcohol, must
be used to make 10 liters of mixture which is 45% alcohol?
What equation will express this problem?
:
Let x = amt of 95% solution
then
(10-x) = amt of 15% solution
:
.95x + .15(10-x) = .45(10)