Needing help with a few beginning alg. questions.

K

koliveri

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Jun 13, 2012
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1
this one is on the formula d=rt i know the formula now im trying to work it backwards. one travels at 40pmh and one travels at 50 mph how many hours will it be till they are 225 miles apart my prof. was kind enough to give me the answe sheet as a test review so i know the answer is 2.5 hours, i am just confused at how to work the problem when i take and try to work it like this


40 mph (rate) so i divide that by the distance 225 i get 5.625
50 mph i get 4.5

so im trying to figure this out any help would be great


2. question im working on is Sam has $8000 to invest. he invest some at 5% APR and some at 8% APR he earns $565 in intrest in one year. How much does he invest at each amount.. answer is $2500 at 5% and $5500 at 8%

i want to figure out how the answer was gotten so i know how to work these.
thanks for your help.
Kris
 
this one is on the formula d=rt i know the formula now im trying to work it backwards. one travels at 40pmh and one travels at 50 mph how many hours will it be till they are 225 miles apart
Click to expand...

Since one travels at 40 mph and the other at 50 mph, the *difference* in their speeds (rates) is 10 mph -- if they are both headed in the same direction. That means that from the viewpoint of the slower one, it looks like the faster one is moving away at 10 mph. Make sense? Therefore, we want to know how long it takes for them to be 225 miles apart when they are separating at a rate of 10 mph.

If we rearrange the distance formula to solve for t, it becomes t = d/r. If we apply that to this problem, it becomes t = 225mi/(10 mph) = 22.5 hours.

However, you did not specify the directions they were moving in, relative to each other. If they are moving in opposite directions, then the relative difference is 40 + 50 = 90 mph. Applying t = d/r again, we get t = (225 miles)/(90 mph) = 2.5 hours. This is the situation that agrees with the answer you were given.

If the future, please be very careful to state problems exactly as they are worded in the problem statement.

Hope that helps.
 
koliveri said:
2. question im working on is Sam has $8000 to invest. he invest some at 5% APR and some at 8% APR he earns $565 in intrest in one year. How much does he invest at each amount.. answer is $2500 at 5% and $5500 at 8%

i want to figure out how the answer was gotten so i know how to work these.
thanks for your help.
Kris
Click to expand...


Start:

Name things to be found. Here you need to find:

How much does he invest at 5% APR → let the amount invested at 5% = F

How much does he invest at 8% APR → let the amount invested at 8% = E

Then we know Sam has $8000 to invest → E + F = 8000 ................................................(1)

We also know he earns $565 in intrest in one year → 0.08*E + 0.05*F = 565 ................................................(2)

Now solve for E & F using (1) and (2)
 
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