Algebra help?

Question

10: Jacob left Seattle and drove his car at thirty-five mph. Caleb wanted to catch up with Jacob but left from the same point at 4:04, which was 1.37 hours later. Caleb traveled at a speed that was sixteen mph more than Jacob did. At what time will Caleb catch up with Jacob?
Hint: express Jocob's time in hours first. Then set the distances expressions equal.
When you have solved for Caleb's time, please round the value to a whole number, then continue.








7:04
4:37
5:29


11: Thomas invested some of his $1,650 at 8% and the rest at 7% for one year. The annual simple interest from the 7% investment exceeds that from the other investment by $12. How much money was invested at 7%?
HInt: the interest from the 7% account is $12.00 more than the 8% account. Therefore, the interest from the 8% account plus $12.00 equals the interest from the 7% account.





$829.00
$960.00
$1,259.00


12: Cameron invested three times as much money at 7.95% as he invested at 6.5%. If his yearly simple interest is $282.26, how much money was invested at 6.5%?
Hint: Find an interest expression for each account. Then, those expressions added together equal the total interest.





$860.00
$900.00
$930.00

Answer 1

Use the formulas:

y = mx + b
e = mc^2

Answer 2

10) Jacobs left 1.37 hours earlier than Caleb, travelling at 35mph. So he had a 35x1.37 = 47.95 mile head start. Caleb was travelling 16 mph faster than Jacobs, so he will close the gap in 47.95/16 = 3 hours. Since Caleb started the race at 4:04 he catches up with Jacobs at 7:04.

11) Lets let M be the amount invested at 7%. The interest at 7% is (0.07)M. Then the amount invested at 8% is 1650-M. The interest at 8% is (0.08)(1650-M). From the problem we know that:
(0.08)(1650-M)+12=(0.07)(M). So we solve for M.
8(1650-M)+1200 = 7M
13200 - 8M + 1200 = 7M
15M = 14400
The amnount invested at 7% M = 14400/15 = $960

12) The amount invested at 6.5% = A. The interest at 6.5% is (0.065)A. The amount invested at 7.95% is 3A. The interest at 7.95% is (0.0795)3A. The total yearly interest is the sum of these two so:
(0.065)A+(0.0795)3A = 282.36
(0.065+0.2385)A = 282.36
0.3035A = 282.36
The amount invested at 6.5% A = 282.36/0.3035 = $930

Answer 3

10

How far did Jacob get in the first 1h37min at a speed of 35mph
distance = velocity *time =35*1.61hours = 56.58 miles.
Now Calab leaves travelling 16 mph faster.
rearange equation, time = distance / velocity = 3.53hours
Round this down becomes 3 hours and add it to the start time 4:04 +3 =7:04
Celeb caught up with Jacob at 7:04


11
let a = investment 1 at 7%
b = investment 2 at 8%
a+b=1650
a*0.07-b*0.08=12
now solve it:
b=(a*0.07-12)/0.08
substitute into a+b=1650
a+(a*0.07-12)/0.08=1650
resolves to
a=960
$960 was invested into the 7% interest account

12
not that different from 11
let investment 1 = a and 2=b
a*.0.0795=i1
b*.0.065=i2
i1+i2=a*0.0795+b*0.065=282.26
now find the intial investment
3b=a
substitute this into the interest equation (=282.26)
3b*0.0795+b*0.065=282.26
resolves to
b=930
$930 was invested into 6.5% interest accont

Jon

Answer 4

#1)Distance travelled by jacob in 1.37 hrs
=1.37*35 km
Relative speed between Jacob and Chaleb=16 km
Therefore,time reqd. for LChaleb to catch up jacob
=1.37*35/16
=3 hrs
Jacon will be caught up at 4-04+3-00 or at 7-04
#11)Let the amount invested at 7% be x
Therefore,amount invested @8%= 1650-x
By the problem,
.07x=(1650-x)*.08 +12
=>.07x=132-0.08x+12
=>0.15x=144
=>x=144/0.15=$960
Thomas invested $960 @7%
#12)Let the investment @6.5% be $x
therefore investment@7.95 is $3x
By the problem,
0.065x+3*0.0795x=$282.26
=>0.065x+0.2385x=282.26
=>0.3035x=282.26
=>x=282.26/0.3035=$930
He invested $930 @ 6.5%

Answer 5

Too many questions. The top one scrolls off the page.
10 - IF seatle is 99 miles away the he won't catch him.
11 - He had x less, so he had 1600-x at 7 and x at 8.
He couldn't equate the two so he bought pizza at 6.


You shouldn't be so lazy as to group 3 questions into 1.

Answer 6

10)
s=d/t
35=d/1.37
35*1.37=d
47.95=d
driving at 16mph more than jacob 47.95/16=3 hours to catch up
so leaving at 4:04 taking 3 hours makes 7:04

answer 7:04

11)
1.08x+12=1.07y
x+y=1650
y=1650-x
1.08x+12=1.07(1650-x)
1.08x+12=1765.5-1.07x
2.15x=1753.5
x=815.58
y=1650-x
y=1650-815.58
y=834.42

i make the answer 834.42

12)

0.0795*3x+0.065*x=282.26
0.2385x+0.065x=282.26
0.3035x=282.26
x=930

answer =930