how does the author get this answer

[allegansveritatem]

The Problem: A swimmer takes 2 hours to swim 10 miles with the current. It takes him/her 4 hours to swim the same distance back against the current. How fast is the current.

I worked it out thus:

2x + 2y = 10
4x - 4y = 10

I multiplied the top equation by 2:

4x + 4y =20
4x - 4y = 10

this led to:

8x= 30, x = 15/4

I put this into the first equation:

2(15/4) + 2y = 10 and multiplied this by 2:

4(15/4) + 4y = 20 which goes to:

15 + 4Y = 20 and eventuates in:

y = 5/4

So the current comes to 5/4 miles. I can't get around this result. but my author, Robert Blixer, gives 15/8 or 1 7/8 as the correct answer. How did he get this? What am I doing wrong here?

I include here a copy of the problem:

 

[Deleted member 4993]

The Problem: A swimmer takes 2 hours to swim 10 miles with the current. It takes him/her 4 hours to swim the same distance back against the current. How fast is the current.

I worked it out thus:

2x + 2y = 10
4x - 4y = 10

I multiplied the top equation by 2:

4x + 4y =20
4x - 4y = 10

this led to:

8x= 30, x = 15/4

I put this into the first equation:

2(15/4) + 2y = 10 and multiplied this by 2:

4(15/4) + 4y = 20 which goes to:

15 + 4Y = 20 and eventuates in:

y = 5/4

So the current comes to 5/4 miles. I can't get around this result. but my author, Robert Blixer, gives 15/8 or 1 7/8 as the correct answer. How did he get this? What am I doing wrong here?

I include here a copy of the problem:View attachment 9408

That is incorrect.

How did you derive those?

Let

the speed of the swimmer = s

the speed of the current = c

then:

10/(s+c) = 2 ................................eqn # 1

and

10/(s - c) = 2*4................................eqn # 2

Now continue......

The answer in the book is correct.

 

[allegansveritatem]

Your "4 hours" should be 8 hours: author specified 4 times longer.
1 7/8 is correct.
Good news: you'd be correct IF 4 hours

Oh boy! I must have read that problem 4 times and didn't catch that! haha. Well, hopefully, that's one fast one that won't be pulled on me successfully again. Thanks for pointing it out.

 

[allegansveritatem]

That is incorrect.

How did you derive those?

Let

the speed of the swimmer = s

the speed of the current = c

then:

10/(s+c) = 2 ................................eqn # 1

and

10/(s - c) = 2*4................................eqn # 2

Now continue......

The answer in the book is correct.

yes, that is the procedure I followed...but no amount of correct procedure will save a bad reading of the problem. Well, wait til next time...as we Cub fans used to say in Chicago after every losing season. But, guess what? There came a time when they won the World Series! So, from that, I take hope.