- #1

- 2

- 0

Ken and Bettina Wikendt live in Minneapolis, Minn. Following a severe snowstorm, Ken and Bettina must Clear the driveway and sidewalk. Ken can clear the snow by himself in 4 hours. Bettina can clear the snow by herself in 6 hours. After Bettina has been working for 3 hours, Ken is able to join her. How much longer will it take them working together to move the rest of the snow.

The book gives the answer as:

t/6 + (t+3)/4 = 1,

thus t = 3/5 of an hour to complete the rest of the job.

When I worked the problem I set it up as follows:

(t+3)/6 + t/4 = 1.

Which works out as t = 1 and 1/5 hours to complete the rest of the job.

At first I figured I just worked the problem wrong, but after reviewing it, I'm not sure if I'm wrong or the book is wrong.

I used "t" as the time they have been working together. So "t+3" equals the total amount of time Bettina has been working.

So using the formula "amount of work = rate * time" with Bettina's rate of 1/6 the total job per hour, and a working time of "t+3" that means the amount of work she did was "(t+3)* 1/6" or simply "(t+3)/6"

For Ken's the amount of work equals "t * 1/4" or simply "t/4"

The total job, "1" should be Ken's work plus Bettina's work, which is "(t+3)/6 + (t/4) = 1"

Working this I get 1 and 1/5 hours for "t"

I even tried working the problem from a diffent angle.

Since after 3 hours Bettina will have completed half the job ("3 * 1/6 = 3/6")

I can figure out the time left by simply firguring out how much time it takes Ken and Bettina to finish the other half of the job. Or simply: "t/6 + t/4 = 1/2". Again, I get 1 and 1/5 hours, NOT 3/5 of an hour.

Is the book wrong or am I?

Thanks,

Ben