1. It takes Dustin 2 hours to shovel the snow from his driveway and sidewalk. It takes his sister 3 hours to shovel the same area. How long will it take them to shovel the walk if they work together?
A: Working together, Dustin and his sister can shovel the walk in 1 1/5 hours, or 1 hour and 12 minutes?
2. A chemistry student needs to make a solution that is 70% water and 30% hydrochloric acid. The student's current mixture of 300 ml is 60% water and 40% hydrochloric acid. How much water must the student add to achieve his desired solution?
A: ?
A: ?
1. T = T1*T2/(T1+T2) = 2*3/(2+3)=1.2 h.
2. H = 0.4 * 300 = 120 mL in current
solution.
W = 0.6 * 300 = 180 mL of water in current solution.
W/(W+H) = 0.7
W/(W+120) = 0.7
W = 0.7W + 84
0.3W = 84
W = 280 mL of water in new solution.
280-180 = 100 mL of water added to new
solution.
To solve this problem, we need to calculate how much water the student needs to add to achieve a 70% water solution.
Step 1: Determine the amount of hydrochloric acid in the current mixture.
If the current mixture is 300 ml and it is 40% hydrochloric acid, then the amount of hydrochloric acid in the mixture is 300 ml * 0.4 = 120 ml.
Step 2: Determine the amount of water in the current mixture.
If the current mixture is 300 ml and it is 60% water, then the amount of water in the mixture is 300 ml * 0.6 = 180 ml.
Step 3: Determine the total desired volume of the final solution.
Since we want to find out how much water the student needs to add, the total desired volume of the final solution will still be 300 ml.
Step 4: Calculate the amount of water needed to achieve a 70% water solution.
To find this, we need to subtract the amount of hydrochloric acid in the current mixture from the total desired volume of the final solution.
So, 300 ml - 120 ml (amount of hydrochloric acid) = 180 ml.
Therefore, the student needs to add 180 ml of water to achieve a 70% water and 30% hydrochloric acid solution.