I need help.... sooo bad.... thanks!?

Question

1.A truck traveling at a constant rate of 45 miles per hour leaves Middletown. One hour later a car traveling at a constant rate of 60 miles per hour also leaves Middletown traveling in the same direction on the same highway. How long will it take for the car to catch up to the truck, if both vehicles continue in the same direction on the highway?

2.Ben had twice as many nickels as dimes. Altogether, Ben had $4.20. How many nickels and how many dimes did Ben have?

3.Vincent has cut three pieces of rope to complete a science project. Two pieces are of equal length. The third piece is one-quarter the length of each of the others. He cut the three pieces from a rope 54 meters long without any rope left over. Find the number of meters in each piece.

Answer 1

[1] the formula d=rt means distance travelled equals rate of speed multiply time
the trucks distance 45(t)
the cars distance 60(t-1) since it started one hour later.
the car catches the truck when they have traveled the same distance so
45 t = 60(t-1) solve for time (t)
[2] n is nickels and d is dimes
n = 2d and 5n + 10d = 420 for money value
substitute for n in second equation and get
5(2d) + 10d = 420 solve this for dimes (d)
and finish
[3] x is length of each of the two pieces that are equal length
x + x + (1/4)x = 54 solve this

Answer 2

1) In 1 hour, the truck is 45 miles from Middletown, the car is 0. In 2 hrs, the truck is 90 miles from Middletown, and the car is 60. In 3 hours, the truck is 135 miles from Middletown and the car is 120. In 3 hours, the truck is 180 miles from Middletown and the car is 180.Notice that the difference between their positions decreases by 15 miles each time. This is because the car is moving 15 mph faster than the truck. Therefore, 45/3+1 is the answer - 4 hours.

2) 2 nickels = 1 dime, 2x nickels = x dimes. They're the same thing. Therefore, divide $4.20 by 2 to get a quotient of $2.10. Then, divide $2.10 by 10 for 21 dimes, and the other $2.10 by 4 for 42 nickels. Ben, therefore, has 21 dimes and 42 nickels.

3) The first and second pieces individually equal x, together equaling x2. If the 3rd piece equals y, then y4 = x and x2 + y = 54. Rewrite x2 + y as x + x + y, then as y4 + y4 + y1. Therefore, 54 = y9. 54 divided by 9 is 6. Therefore, the first and second piece are each 6 * 4, or 24 meters long, and the 3rd piece is 6 meters long.

Answer 3

a. 3 hours
the truck has an advantage of 45 miles but the car movesat a faster speed of 15 miles per hour so for the car to catch up when both of them are driving at a constant speed is 3 hours

b. 21 dimes, 42 nickels.

c. 24 metres for the first two pieces, 6 meters for the last piece

hope im right

Answer 4

1, difference in speed is the rate at which the cars will close in on each other so we only need that speed
60mph - 45mph = 15mph
car had a 1hr head start, so their is 1 hr worth of distance between them (1hr * 45mph = 45 miles)

Question is really asking how longwill it take you to go 45 miles if you are goign 15 miles an hour

ANS: 3 hrs

2,
2nickels = same as 1 dime, so nickels = 1/2 and dimes = 1/2
$4.20 /2 => $2.10 in nickels and $2.10 in dimes

ANS: 21 dimes and 42 nickels


3,
2n + n/4 = 54
8n + n = 216
9n = 216
n = 216/9 = 24
pieces are 24, 24, 24/4=6

ANS: 24m, 24m, 6m

Answer 5

Hello,

1. dt = 45*t
dc = 60*(t-1) since the distances are equal when they meet so 45t = 60(t-1) 45t = 60t -60 so -15t = -60 or t = 4


2. n = 2d
5n + 10 d = 420

so 5(2d) + 10 d = 420 then 20d = 420 and d = 21 so n = 42


3. l + l + 1/4l = 54 so 2 1/4 l = 54 then l = 24 and 1/4 l = 6 meters


Hope This Helps!

Answer 6

#2-
nickles are half the amout of dimes
so if you divide $4.20 by .10 you get how many dimes you need (with no other coins)
then you take that number divide it by 2 and take that number and divide it by .05 and i think u get the right answer yep
so u have:
42 nickles
21 dimes

Answer 7

wow so much?

lol its ok i do the same :)