word problems?

Question

1.
In a certain mixture, the ratio of glycol to water is five to three. If ten ounces of glycol are added to the mixture, it becomes seventy percent glycol. How many ounces of glycol are in the original mixture?

2.
One person can do a certain job in one-half hour, and another person can do the same job in one hour and ten minutes. How many minutes will thet take to do the job together?

Answer 1

1)
The original ratio is 5/3. Let's say that you had 5x ounces of glycol to 3x of water. Then adding 10 ounces, it becomes 7/3. So...

(5x + 10)/3x = 7/3

Multiply by 3x to eliminate denominators:

(5x + 10)/3x = 7/3
5x + 10 = 7x
10 = 2x
x = 5

Since x=5, and you had 5x ounces of glycol in the original mixture, you had 25 ounces of glycol.

2)
The first person does 1 job / 0.5 hours = 2 jobs/hour.
The second person does 1 job / 7/6 hours = 6/7 jobs/hour

Together they do 2 + 6/7 jobs/hour. The number of minutes required for them to do a job is:

60 * ( 1 / (2 + 6/7) ) =
60 * ( 1 / (20 / 7) ) =
60 * 7/20 =
21 minutes

Answer 2

2. 60/(60/30 + 60/70) = 21 minutes