I have 2 questions in math that I am not quite sure about...
1. Mandy begins bicycling west at 30 mph at 11 A.M. If Liz leaves from the same point 20 min. later bicycling west at 36 miles per hour, when will she catch Mandy?
2. A mixture of 10% acid and 90% water is added to 5 liters of pure acid. The final mixture is 40% water. How many liters of water are in the final mixture?
thanks:)
1. Write equations for distance traveled vs. the time after 11 AM. Set them equal and solve for t.
M = .5 t (if t is in minutes)
L = .6 (t -20)
M = L when 0.5t = 0.6t -12
0.1t = 12
t = 120 minutes (after 11 AM), which is 1:00 PM
2. Assume X liters of 10/90 mix are added
Liters of acid in mix = 0.1X + 5
Liters of water in mix = 0.9X
Total volume of mix = 5 + X
Solve 0.4 = 0.9X/(5+X)
2 + 0.4X = 0.9X
X = 4
90% of X is the amount of water
No problem! I'll be happy to help you with both of your math questions.
Question 1:
To find when Liz will catch up to Mandy, we need to determine the time it will take for Liz to travel the same distance as Mandy. Since both are traveling in the same direction, their relative velocity will be the difference of their speeds.
1. First, convert Mandy's time of departure to minutes: 11 A.M. is 11 * 60 = 660 minutes.
2. Since Liz leaves 20 minutes later, her time of departure is 660 + 20 = 680 minutes.
3. Now we'll calculate the distance Mandy has traveled by the time Liz departs. We know that Distance = Speed * Time. So, for Mandy, Distance = 30 mph * (680 minutes / 60 minutes/hour) = 340 miles.
4. Similarly, Liz's distance is unknown, denoted as d. We can set up the equation: Distance = Speed * Time. So, 36 mph * T = d, where T is the time it will take for Liz to catch Mandy.
5. Since Liz is trying to catch up to Mandy, we know that Liz's distance will be the same as Mandy's distance when they meet. Therefore, d = 340 miles.
6. Now we can solve the equation: 36 mph * T = 340 miles. Divide both sides by 36 to isolate T: T = 340 miles / 36 mph ≈ 9.44 hours.
7. The time Liz catches up to Mandy is 9.44 hours after she starts, or 680 + 9.44 = 689.44 minutes after 11 A.M. Approximately, this is 11:29 A.M.
Therefore, Liz will catch Mandy at approximately 11:29 A.M.
Question 2:
To find the number of liters of water in the final mixture, we can set up an equation using the concept of the amount of acid in the initial solution and the final mixture.
Let's denote the final amount of water in the mixture as W liters.
1. The initial mixture of 5 liters of pure acid consists of 10% acid and 90% water. Therefore, it contains 0.10 * 5 = 0.50 liters of acid and 0.90 * 5 = 4.50 liters of water.
2. The final mixture is 40% water, which means the amount of acid in the final mixture is 60%.
3. We can set up the equation: 0.40 * (5 + W) = 0.50, where 5 + W is the total volume of the final mixture.
4. Distribute the 0.40 on the left side of the equation: 2 + 0.40W = 0.50.
5. Subtract 2 from both sides of the equation: 0.40W = 0.50 - 2 = -1.50.
6. Divide both sides of the equation by 0.40 to solve for W: W = -1.50 / 0.40 = -3.75 liters.
It seems like we've encountered a problem because the result is a negative number. This implies that the given conditions are not feasible or there might be an error in the question. Please double-check the question and the given information to ensure accuracy.
If you have any further questions, feel free to ask!