SOLUTION: Can anyone help me with these 4 problems please? And if you could, please show your work as well. Thank you! ~Sarah 1. A radiator contains 6 quarts of a mixture of antifreeze

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Question 209931: Can anyone help me with these 4 problems please? And if you could, please show your work as well. Thank you! ~Sarah

1. A radiator contains 6 quarts of a mixture of antifreeze and water. 40% of this mixture is antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that the mixture will be 60% antifreeze?

2. A car (Car A) leaves a gas station and travels along a straight road 200 miles long at a uniform speed of 40 miles per hour. A second car (Car B) leaves the station 1/2 hour later and travels along the same road at 55 miles per hour. At what time will Car B overtake Car A?

3. How much water must be evaporated from 500 grams of a 10% salt solution to obtain a 15% salt solution?

4. A boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes. How long will it take for both mowing at the same time to mow the lawn?

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
. A radiator contains 6 quarts of a mixture of antifreeze and water.
40% of this mixture is antifreeze. How much of this mixture should be drained
and replaced with pure antifreeze so that the mixture will be 60% antifreeze?
:
Let x = amt to be removed and to be added
:
.40(6-x) + x = .60(6)
2.4 - .4x + x = 3.6
-.4x + x = 3.6 - 2.4
.6x = 1.2
x = 1.2/.6
x = 2 qts removed and 2 qts of pure antifreeze added
:
:
2. A car (Car A) leaves a gas station and travels along a straight road 200
miles long at a uniform speed of 40 miles per hour.
A second car (Car B) leaves the station 1/2 hour later and travels along the
same road at 55 miles per hour. At what time will Car B overtake Car A?
:
Let t = travel time of car B
then
(t+.5) = travel time of car A
:
When B catches A, they will have traveled the same distance
Write a distance equation: Dist = speed * time
55t = 40(t+.5)
55t = 40t + 20
55t - 40t = 20
15t = 20
t = 20/15
t = 1 hrs travel time when of Car B
:
:
3. How much water must be evaporated from 500 grams of a 10% salt solution to obtain a 15% salt solution?
:
Let x = amt of water to be evaporated
.10(500) = .15(500-x)
50 = 75 -.15x
50 - 75 = -.15x
-25 = -.15x
x = 25/.15
x = 166 grams to be evaporated
:
:
4. A boy can mow a lawn in 90 minutes and his sister can mow the same lawn in 60 minutes. How long will it take for both mowing at the same time to mow the lawn?
:
Let t = amt of time working together
Let the completed job = 1
+ = 1
Multiply equation by 180 to get rid of the denominators
2t + 3t = 180
5t = 180/5
t = 36 min working together