Bernice Said:

I have 3 math problems. Can YOU help?

We Answered:

Though it may seem difficult, the questions are simply asking for the rate at which each individual complete the task. Once you figure that out, you can add all 3 rates together and come up with the combined total.

1. Sam took 4 days for the job. So he/she makes 1/4 of the total progress per day.
Lisa took 6 days for the job. So she makes 1/6 of the total progress per day.
Tom took 2 days for the job. He makes 1/2 of the total progress per day.

Add all three rates together, 1/2 + 1/6 + 1/4 = 11/12. This is the rate at which all 3 persons would complete the job on a per day basis.

The job will come to a finish when it reaches 1 (100%), divide that by the rate of 11/12 (92.58%) done per day and you get 1.09 days for an answer.

2. Steven: 20/5 = 4 drinks/min
Sue: 20/10 = 2 drinks/min
Jack: 20/15 = 4/3 drink/min

Again, add all 3 rates together but this time the divisor is 20 because you're solving for how long it would take for all 3 to mix 20 drinks.

4 + 2 + 4/3 = 7 and 1/3 (total combined rate for all 3 working together)

20 / (7 and 1/3) = 2.7272... minutes = 164 seconds (2 minutes 44 seconds)

3. Convert minutes to hours because we want all values in the same units.

Jim: 30 minutes = 0.5 hour = 2 fills per hour
Sue: 45 minutes = 0.75 hour = 4/3 fills per hour
Tony: 1 and 1/2 hour = 2/3 fills per hour

2 + 4/3 + 2/3 = 4 fills per hour

If they can fill the pool four times in one hour, then it means that they can do it once every 15 minutes.

Joyce Said:

How do you solve these types of problems? explain thoroughly!!!?

We Answered:

For these you need to think of them all in terms of the rate that things are being done. In question 1, it takes Same 4 days to finish a house, so he works at 1/4 of a house per day. 1/4 + 1/6 + 1/2 = 11/12 of a house per day. The inverse (12/11) is how many days it takes to complete 1 house. Approx 1.09

Steven mixes 4 drinks per minute; Sue mixes 2 drinks per minute; Jack mixes 4/3 drinks per minute. Combined they mix 22/3 drinks per minute. 20 divided by 22/3 = approx 2 minutes 44 seconds

Jim = 1/30 pool per minute; Sue = 1/45 pool per minute; Tony = 1/90 pool per minute. Combine = 1/15 pool per minute. So, 15 minutes to fill the pool