Word Problems/Unit Rate

Advertisement


Question
Hello:

Have I determined the unit rate for the following correctly?

If 4 pipes can drain a tank in 70 minutes, how long will it take 1 pipe to drain the same tank?

Since 1 pipe will take longer than 4 pipes, is the following solution correct?

(4/1) X 70 minutes/(1/4) X 4 pipes will equal 280 minutes/1 pipe.

I think that the quantities are inversely proportional to each other.
The inverse of 4 is 1/4.

Usually to find the unit rate, divide the numerator and denominator by the denominator. In this situation, this method will not produce the correct answer because of the inverse relationship.

I thank you for your reply.

Answer
Since the number of pipes times the amount of time is a constant, multiplying the 1st constant by a factor means we need to divide the 2nd by the same factor.

If we have ab = C, then we would have (2a)(b/2) = C, (3a)(b/3) = C, (na)/(b/n) = C, etc.

Problems like this all come down to the units involved.  This can be learned really well by looking at physics problems.

The tank has some volume measured in gallons, referred to as g.
The drainage rate of a pipe would be in gallons / minute, or r = g/m.

Since the result desired is in minutes, this can be seen to be gotten as g / r
since the units of r are g/m.  Putting this in gives g/(g/m) = 1/(1/m) = m,
and that is what is trying to be found.  

Word Problems

All Answers


Answers by Expert:


Ask Experts

Volunteer


Scott A Wilson

Expertise

I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.

Experience

My experience is from when I started doing story problems in grade school. I have been assisting, helping, and bringing smiles to many others ever since. Are you the next one?

Publications
In over 850 questions answered to other users. Maybe you're the next one ...

Education/Credentials
I received a BA in Mathematical Sciences from OSU and a MS in Mathematics from OSU as well.

Awards and Honors
I earned Both my BS degree and MS degree with honors for having such a high grade point average.

Past/Present Clients
I have answered hundreds and hundreds of students at OSU in the 80's and over 8,500 questions right here, but only a little over 850 of them have been word problems.

©2016 About.com. All rights reserved.