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#1 2015-04-05 03:23:49

jubadedo
Guest

Rate Problems

Hi guys,
these two problems just keep throwing me off. I think I'm setting them up completely wrong.

1. Three window washers can wash 6 windows in 60 minutes. How many windows could 5 window washers wash in 90 minutes if they work at the same rate as the 3 window washers?


2. Miss White hires Sleepy and Dopey to pick apples from her orchard. The two of them can pick three crates of apples in four hours. If she hires five more pickers, how many crates of apples could the seven pickers pick in eight hours working at the same rate as Sleepy and Dopey?

#2 2015-04-05 05:34:51

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Rate Problems

hi jubadedo

Welcome to the forum.

You need to think about whether a change in one variable will cause the same change or the inverse change in another.

For example if the number of windows goes up, then the time taken will go up as well.  If the number of people goes up, then the time taken will go down.

Q1.  Three washers has gone up to 5 washers.  More windows can be washed, so that will increase by a factor of 5/3

The time has gone up too, from 60 mins to 90 mins.  Again more windows can be washed, so that will increase by a factor of 90/60.

Putting these two factors together means:

Q2.  Pickers goes up from 2 to 5+2=7 so the factor for that is x 7/2
Times goes up from 4 hours to 8 hours so that's x 8/4

In general an increasing factor is (what it has become)/(what it was.)

Further example.

If the apples problem was how many pickers are needed to pick 6 crates in  8 hours.

More crates so it will require more pickers with a factor of x 6/3

More time  so it will require less pickers with a factor of x 4/8

Note I have inverted the fraction because as time goes up, the number of pickers will go down.

Hope that helps.  If you want to post your answers, I'll check them for you.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2015-04-05 13:20:43

jubadedo
Member
Registered: 2015-04-05
Posts: 19

Re: Rate Problems

Thanks a lot Bob for explaining it so clearly big_smile. I understand what the questions means now.
I got 15 windows for the first question and 21 crates for the second question. Is that correct?

Last edited by jubadedo (2015-04-05 13:21:02)

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#4 2015-04-05 19:36:32

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

Re: Rate Problems

hi jubadedo

Both answers correct!  Well done!

Sometimes a variable will cause the new total to go down, so watch out for those.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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