Expert: Paul Klarreich - 12/1/2008

Question
John could play 5 holes of golf in 20 minutes and Allan could play 6 holes in 30 minutes. How many minutes would it take them to  play 18 holes if John started playing 2 minutes before Allan joined in?
This is what I did. Is this correct?
J: (18 holes)(20 min)/(5 holes) = 72 min.
A: (18 holes)(30 min)/(6 holes) = 90 min.
J starts 2 min. before A, so the total time is 90 + 2 = 92 min.
Thank you for your help!

Answer
Questioner:   Keli
Category:  Calculus
Private:  No
 
Subject:  Pre-calc word problem
Question:  John could play 5 holes of golf in 20 minutes and Allan could play 6 holes in 30 minutes. How many minutes would it take them to  play 18 holes if John started playing 2 minutes before Allan joined in?

This is what I did. Is this correct?

J: (18 holes)(20 min)/(5 holes) = 72 min.
A: (18 holes)(30 min)/(6 holes) = 90 min.

J starts 2 min. before A, so the total time is 90 + 2 = 92 min.
Thank you for your help!
............................................  

Hi, Keli,

I am not sure.  Your interpretation is:

How long will the golf game take, assuming they must EACH complete the 18-hole course?  (which is the way normal golfers would do it, if there are such people)

But I think your teacher wants you to do this as a rate-time-work problem, like this:

John could grind 5 pounds of wheat in 20 minutes and Allan could grind 6 lbs in 30 minutes. How many minutes would it take them to grind 18 pounds if John started playing, .. er,.. grinding 2 minutes before Allan joined in?

Now you will do the following:


John grinds 1 lb in 4 mins, so 0.25 lbs per min.(his rate)
Allan: 1 in 5 mins, so 0.2 lbs per min.

Let x + 2 = the length of time that John grinds.
and x  = the length of time that Allan grinds.

0.25(x + 2) + 0.2x = 18

Now you solve.