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. To solve the first question, we need to understand that both Mandy and Liz are cycling in the same direction. The key to solving this problem is recognizing that since Liz started 20 minutes later, Mandy has a head start in terms of distance.
Let's set up an equation to represent the distance each person covers until they meet. We can use the formula: Distance = Speed * Time.
Consider the time it takes for Liz to catch up to Mandy as 't' hours. Since Mandy starts 20 minutes earlier, she cycles for (t + 1/3) hours (20 minutes = 1/3 hour).
For Mandy: Distance = Speed * Time = 30 * (t + 1/3)
For Liz: Distance = Speed * Time = 36 * t
Since they meet at the same point, the distances covered by both Mandy and Liz are equal. Therefore, we can set up the equation:
30 * (t + 1/3) = 36 * t
Now we can solve for 't'.
30t + 10 = 36t
10 = 6t
t = 10/6
t = 5/3
So Liz will catch up to Mandy in 5/3 hours, or 1 hour and 40 minutes after Liz starts her journey at 11:20 A.M.
2. To solve the second question, we need to find the amount of water in the final mixture. Let's set up the problem step by step.
Initially, there are 5 liters of pure acid. Since the final mixture is 40% water, this means that 60% of the mixture is acid.
Let 'x' be the amount of water we need to add to the initial 5 liters of pure acid.
So, the total volume of the final mixture will be 5 liters (pure acid) + x liters (water).
Since the mixture is 10% acid and 90% water initially, we can set up the equation:
(10% of 5) + x = 60% of (5 + x)
0.1 * 5 + x = 0.6 * (5 + x)
0.5 + x = 3 + 0.6x
0.4x = 2.5
x = 2.5 / 0.4
x = 6.25
Therefore, 6.25 liters of water need to be added to the initial 5 liters of pure acid to obtain a final mixture that is 40% water.