Question

Please, will someone check my answers and help me solve the other questions?


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: ?

Solve. Check your answer.

3. ((d + 2)/(d + 8)) = ((-6)/(d + 8))

A: ?

4. 4/n^2 = 7/n + 2

A: n = -4 or n = 1/2?

5. 2/t + 4/3t = 4/t + 2

A: t = 10?

6. ((x -6)/(x^2-6)) = ((-4)/(x-4))

A: ?

Answer 1

let the amount to be added by x ml
so we have 300+x ml of the new mixture

.3(300+x) = .4(300)
3(300+x) = 4(300)
900 + 3x = 1200
3x = 300
x = 100

Add 100 ml of water

check:
Do we have the correct amount of acid?
in original: .4(300) = 1200 ml
in new: .3(400) = 120 ml -----> correct

what about the concentrtion of water?
in original: .6(300) = 180 ml
in new : .7(400) = 280 ml ----> 100 ml more, of coure we added that

1. I do that kind this way
Consider the whole job to be 1
Dustins rate = 1/2 jobs/hr
sisters rate = 1/3 jobs/h

combined rate = 1/2 + 1/3 = 5/6
time to do 1 job at combined rate
= 1/(5/6)
= 6/5 hrs , which is 1 hr, 20 minutes, which you had