I have these math word problems I can’t figure out! Please help, they’re due soon! Any help is welcome

Question

1. One morning, Justin drove 5 hours before stopping to eat lunch at Chick-fil-A. After lunch, he increased his speed by 10 mph. If he completed a 370-mile trip in 7 hours of driving time, how fast did he drive in the morning?

2. Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 44 mph. When Allison arrived, Austin still had 70 miles to go. How far did Allison drive?

3. Kevin stuffs shrimp in his job as a seafood chef. He can stuff 1,500 shrimp in 4 hours. When his sister helps him, they can stuff 1,500 shrimp in 3 hours. If Kevin gets sick, how long will it take his sister to stuff 750 shrimp?

4. One crew can seal a parking lot in 12 hours and another in 16 hours. How long will it take to seal the parking lot if the two crews work together?

5. Equal amounts are invested at 4%, 7%, and 9% annual interest. If the three investments yield a total of $880 annual interest, find the total investment.

6. An executive invests $27,000, some at 5% and the rest at 4% annual interest. If he receives an annual return of $1,200, how much is invested at each rate?

Answer 1

ya killin us Emily!!!

1) 185 miles one way....

distance = rate * time

R is the intial speed

t is the time on the return trip

185 = R*(7-t)

= (r+10)*t

185/r = 7-t

185/(r+10) = t

7 = 7-t + t = 185/r + 185/(r+10)

7/1 = 185/r + 185/(r+10)

multiplies everything by common denominator is r(r+10)

7r(r+10) = 185(r+10) + 185r

7r^2 + 70r = 185r + 1850 + 185r

7r^2 + 70r = 370r + 1850

7r^2 + 70r - 370r - 1850 = 0

7r^2 - 300r - 1850 = 0

r = [300 + sqrt( 300^2 + 4*7*1850)] / 14

= [300 + sqrt(90000 + 51800)]/14

= [ 300 + sqrt( 141800)]/14

= [ 300+ 10* sqrt(1418)]/14

= [ 300 + 10*sqrt(2*709)]/14 <-- 709 is prime

= [ 150 + 5*sqrt(1418)]/7

= 48.325957691089614760609342574044

then t= 185/(r+10)

= 185/(58.325957691089614760609342574044...)

= 3.1718296162372696675734601981694...

3 hours + 10 mins + 18.586618454170803264456713409714... secs

Morning: 48.325957691089614760609342574044... mph

for t = 7-3.1718296162372696675734601981694 hours

= 3.82817038376273

afternoon: 58.325957691089614760609342574044 mph.... for

t = 3.1718296162372696675734601981694

Yes they multiply to 185

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(2)

D is the total distance...

D = 58*t

D-70 = 44*t

58 t - 70 = 44 t

14t - 70 = 0

14t = 70

t = 5

D = 58*5 = 290

290-70 = 220 = 44*5, so yes it checks

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(3)

Kevin stuffs 375 shrimp per hour

Their combined rate is 500 shrimp per hour

Sister rate is 125 shrimp per hour

It will take her 750/125 = 6 hours

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(4)

work rate of the 1st crew is 1/12 lot per hour

work rate of the 2nd crew is 1/16 lot per hour

combined work rate is (16+12)/192 = 28/192 = 14/96 = 7/48 lot per hour

Working together they will finish the lot in 48/7 = 6 and 6/7 hours

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(5) X is the amount invested....

X/3 is invested in each of the three accounts...

0.04* x/3 + 0.07*x/3 + 0.09 * x/3 = 880

(x/3) ( 0.04 + 0.07+0.09) = 880

(x/3) ( 0.2) = 880

(x/3) (1/5) = 880 <--- 1/5 = 0.2

x/15 = 880

x= 880*15 = 13200

4400 invested in each account...

4% of 4400 = 176

7% of 4400 = 308

9% of 4400 = 396

Total is 880, so it checks

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X is the amount at 5%

27000 - x is the amount at 4%

0.05X + 0.04(27000-x) = 1200

0.05 x + 1080 - 0.04x = 1200

0.01x = 120

x = 12000

12000 at 5% returns = 600

15000 at 4% returns = 600

so yes it checks