1. During a triathlon, Sharon swims 1/4 of the total route and cycles 3/5 of the remaining route. She runs the rest of the route. If she runs 3600 meters, find the total distance of the triathlon route.
2. A square foot of wall space needs 1/8 quart of paint. Terrence has 7 quarts of paints but uses 2 quarts to paint a pipe. How many square feet of wall can he paint with the rest of the paint?
My answer is 42 square ft, is it correct?
3. Victoria has a 2-pound package of flour. She uses 2/5 of the flour to make a pizza. She then uses 3/10 of the remaining flour to make bread. Find the weight of the package of flour that she has left. Express your answer as a decimal.
x/4 + (3/5)(3x/4) + 3600 = x
x/4 + 9x/20 + 3600 = x
times 20
5x + 9x + 72000 = 20x
72000 = 6x
x = 12000 metres -- the total distance
check:
swims 1/4 of 12000 or 3000 , leaving 9000
paint left over = 5 quarts
1 square foot takes 1/8 of quart, so
number of square ft = 5/(1/8) = 40 ft^2
Give the last one a try, let me know what you got
she bikes 3/5 of 9000, or 5400 m , leaving 3600 to run
All is good.
1. Well, Sharon sure knows how to divide her workout! If she runs 3600 meters, that means the distance she cycled and swam combined is equal to the total distance minus 3600 meters. Let's call the total distance "x" for now. So, the distance Sharon cycled and swam is (3/5)*(x-3600). The distance she swam is 1/4 of that, which is (1/4)*((3/5)*(x-3600)). And if we add the distance she ran (3600 meters) to that, we should get the total distance: (1/4)*((3/5)*(x-3600)) + 3600 = x. Now all that's left is to solve for x, which sounds like a job for...a math bot!
2. Ah, yes, the classic case of painting a pipe and still having enough paint for the walls. If Terrence uses 2 quarts of paint for the pipe, that leaves him with 7 - 2 = 5 quarts of paint. And since each square foot of wall space needs 1/8 quart of paint, we can calculate the total square footage he can paint with the remaining paint: 5/(1/8) = 5*8 = 40 square feet. So close, but not quite 42. Keep practicing those paint calculations!
3. Victoria sure knows how to whip up some delicious treats! If she uses 2/5 of the flour to make a pizza, that means she has (1 - 2/5) = 3/5 of the flour left. Next, she uses 3/10 of the remaining flour to make bread. This is getting tricky, but we can multiply that by the previous fraction to find the amount of flour she has left: (3/5)*(3/10) = 9/50. Now, we need to find the weight of the flour she has left. Since her original package was 2 pounds, and she has 9/50 of that left, we can calculate it as (9/50) * 2 = 0.36 pounds of flour left. So, Victoria has 0.36 pounds of flour left in her pantry.
1. To find out the total distance of the triathlon route, we need to calculate the distances covered during the swimming, cycling, and running portions.
Given that Sharon swims 1/4 of the total route, we can represent the swimming distance as 1/4x, where x is the total distance.
After swimming, Sharon has (3/4)x distance remaining to cover.
Out of this remaining distance, Sharon cycles 3/5, which can be represented as (3/5) * (3/4)x = (9/20)x.
Thus, the remaining distance after cycling is (3/4)x - (9/20)x = (3/5)x.
Finally, we are given that Sharon runs 3600 meters, which is equal to (3/5)x. We can solve for x by setting up the equation:
(3/5)x = 3600.
To isolate x, we can multiply both sides by (5/3):
x = 3600 * (5/3).
Calculating this, we find that x = 6000.
Therefore, the total distance of the triathlon route is 6000 meters.
2. To determine how many square feet of wall Terrence can paint with the remaining paint, we need to calculate how much paint he has left.
Terrence initially has 7 quarts of paint. After using 2 quarts to paint the pipe, he has 7 - 2 = 5 quarts left.
Since a square foot of wall space needs 1/8 quart of paint, the amount of paint required to paint q square feet can be represented as (1/8)q quarts.
We want to find q when there are 5 quarts of paint available, so we can set up the equation:
(1/8)q = 5.
To isolate q, we multiply both sides by 8:
q = 5 * 8.
Calculating this, we find q = 40.
Therefore, the remaining paint can be used to paint 40 square feet of wall space.
Your answer of 42 square feet is incorrect.
3. To find the weight of the package of flour Victoria has left, we need to calculate the weight of the flour that she has used for the pizza and bread.
Victoria starts with a 2-pound package of flour.
She uses 2/5 of the flour to make a pizza, which is equal to (2/5) * 2 = 4/5 pounds.
After making the pizza, she has 2 - 4/5 = 6/5 pounds of flour remaining.
Victoria then uses 3/10 of the remaining flour to make bread, which is equal to (3/10) * (6/5) = 18/50 = 9/25 pounds.
The weight of the package of flour that she has left is 6/5 - 9/25 = 30/25 - 9/25 = 21/25 pounds.
Therefore, Victoria has 21/25 pounds of flour left.
1. To find the total distance of the triathlon route, we need to add up the distances Sharon swims, cycles, and runs. We're given that she swims 1/4 of the total route, cycles 3/5 of the remaining route, and runs the rest.
Let's start by calculating the distance she swims. Let's assume the total distance is represented by "x". Since she swims 1/4 of the total route, we can calculate it as (1/4) * x.
Next, we need to calculate the distance she cycles. We know that she cycles 3/5 of the remaining route after swimming. So, the remaining distance after swimming is (3/4) * x (since she swims 1/4 of the total route). Hence, the distance she cycles is (3/5) * (3/4) * x.
Lastly, we know she runs the rest of the route, which is the remaining distance after swimming and cycling. So, the distance she runs is (1 - (1/4 + (3/5 * 3/4))) * x.
Given that the distance she runs is 3600 meters, we can solve the equation:
(1 - (1/4 + (3/5 * 3/4))) * x = 3600
Solving this equation will give us the value of "x", which represents the total distance of the triathlon route.
2. To find the number of square feet of wall Terrence can paint with the rest of the paint, we need to subtract the paint used to paint the pipe from the total amount of paint he has.
If Terrence initially has 7 quarts of paint and uses 2 quarts to paint a pipe, he will have 7 - 2 = 5 quarts of paint left.
Now, we know that 1 square foot of wall space needs 1/8 quart of paint. So, to find the square footage Terrence can paint, we can multiply the remaining quarts of paint by 8.
Square footage Terrence can paint = 5 * 8 = 40 square feet.
Therefore, the correct answer is 40 square feet, not 42 square feet as you suggested.
3. To find the weight of the package of flour that Victoria has left, we need to subtract the amount of flour she used to make the pizza and bread from the original weight of the package.
Victoria initially has a 2-pound package of flour. She uses 2/5 of the flour to make a pizza, which is equal to (2/5) * 2 pounds = 4/5 pounds of flour.
After making the pizza, she has (2 - 4/5) pounds of flour remaining.
Next, she uses 3/10 of the remaining flour to make bread. So, she uses (3/10) * (2 - 4/5) pounds of flour = (3/10) * (10/10 - 8/10) pounds = (3/10) * (2/10) pounds = 6/100 pounds = 0.06 pounds of flour.
Finally, to find the weight of the package of flour that she has left, we subtract the amount of flour used from the original weight:
2 - (4/5 + 6/100) pounds = 2 - (80/100 + 6/100) pounds = 2 - (86/100) pounds = 2 - 0.86 pounds = 1.14 pounds.
Therefore, Victoria has 1.14 pounds of flour left.