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sanding

by Deepthi Subbu » Wed Sep 14, 2011 11:19 pm
Wendy begins sanding a kitchen floor by herself and works for 4 hours .She is then joined by Bruce and together 2 of them finish sanding the floor in 2 hours . If bruce can sand the floor himself in 20 hours , how long will it take wendy to sand the floor by herself ?

Considering Bruce's rate to be r . Since she had worked for 4 hours and since Bruce alone can finish it in 20 hours , my equation goes like this -

4(1/r) + 1(1/20) = 1/2 .

Is there a fault with this ? Pls help
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by shankar.ashwin » Wed Sep 14, 2011 11:33 pm
If Wendy's takes r hrs to complete the work alone,

we have;

4/r + 2( 1/r + 1/20) = 1

4/r -> because Wendy has already worked 4 hrs

2( 1/r + 1/20) because both together work for 2 hrs at rates 1/r and 1/20.

So we can find r = 20/3 (or) 6hrs 40 mins.
Deepthi Subbu wrote:Wendy begins sanding a kitchen floor by herself and works for 4 hours .She is then joined by Bruce and together 2 of them finish sanding the floor in 2 hours . If bruce can sand the floor himself in 20 hours , how long will it take wendy to sand the floor by herself ?

Considering Bruce's rate to be r . Since she had worked for 4 hours and since Bruce alone can finish it in 20 hours , my equation goes like this -

4(1/r) + 1(1/20) = 1/2 .

Is there a fault with this ? Pls help
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by knight247 » Thu Sep 15, 2011 2:28 am
@ashwin
Great job on the solution. Since Ashwin has already solved using algeraic approach. Lets take a smart number approach to this problem

Let the area to be painted be 40 sq.ft
Bruce completes it in 20 hrs i.e. at the rate of 2sq.ft per hr.
When he is working with Sandy he works for exactly 2 hours. So at the rate of 2sq.ft per hr he completes 4 sq.ft.. What remains is 40-4= 36 sq.ft

This 36 sq.ft has to be completed by Sandy alone. How many hours does Sandy work?? Alone for 4 hrs and 2 hrs along with Bruce=6 hrs

R=W/T=36/6= 6 sq ft /hr

6 sq ft ....... 60 minutes
40 sq ft........ ?

Cross multiplying 40*60/6=400 mins=6hrs and 40 minutes
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by Deepthi Subbu » Thu Sep 15, 2011 3:00 am
Lovely , thanks guys.
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