# Ambiguous Problem

• May 12th 2014, 08:04 AM
Vinod
Ambiguous Problem
Hi Members,
This is the problem which I didn't understand.
Miss x walks 35km partly at the rateof 4km/hour and partly at 5km/hour;if she had walked at 5km/hour when she walked at 4km/hour and vice-versa,she would have covered 2 km more in the same time. Find the time she was walking.
Would any member explain me this problem and how to form simultaneous linear equations?
• May 12th 2014, 09:13 AM
romsek
Re: Ambiguous Problem
Quote:

Originally Posted by Vinod
Hi Members,
This is the problem which I didn't understand.
Miss x walks 35km partly at the rateof 4km/hour and partly at 5km/hour;if she had walked at 5km/hour when she walked at 4km/hour and vice-versa,she would have covered 2 km more in the same time. Find the time she was walking.
Would any member explain me this problem and how to form simultaneous linear equations?

This is easily set up incorrectly (as I just did and restarted).

The important thing is that the separate walk times remain fixed.

From the first statement

$4 t_1 + 5 t_2 = 35$ and from the second

$5 t_1 + 4 t_2 = 37$

or

$\begin{pmatrix}4 &5 \\ 5 & 4\end{pmatrix}\begin{pmatrix}t_1 \\ t_2\end{pmatrix} = \begin{pmatrix} 35 \\ 37\end{pmatrix}$
• May 13th 2014, 06:52 AM
Vinod
Re: Ambiguous Problem
Hi romsek,
I have solved $t_{2} = 3 and t_{1} =5$ even before posting this thread but last part of question needs to find out the time she was walking. How is that to be computed?
• May 13th 2014, 07:48 AM
HallsofIvy
Re: Ambiguous Problem
What did you choose " $t_1$" and " $t_2$" to mean when you set up the problem?
• May 13th 2014, 10:34 AM
romsek
Re: Ambiguous Problem
Quote:

Originally Posted by Vinod
Hi romsek,
I have solved $t_{2} = 3 and t_{1} =5$ even before posting this thread but last part of question needs to find out the time she was walking. How is that to be computed?

uhh how about $t_1+t_2$
• May 14th 2014, 07:29 AM
Vinod
Re: Ambiguous Problem
Quote:

Originally Posted by HallsofIvy
What did you choose " $t_1$" and " $t_2$" to mean when you set up the problem?

Solving for $t_1$ and $t_2$ is just like a leap in the dark. It is a shooting of target in the darkness of night.
So, main question is to find out the time she was walking.
One point is clear that Miss x walks 35 kms. partly by 4km/hour and partly by 5km/ hour. Other information given in the problem is unclear to me. Do you know the answer?
• May 14th 2014, 10:25 AM
ebaines
Re: Ambiguous Problem
Vinod - you have already figured out that she walked for 5 hours at one speed and 3 hours at another. So the total time she walked was 5 hours + 3 hours=8 hours. It's not ambiguous at all.
• May 14th 2014, 04:40 PM
Vinod
Re: Ambiguous Problem
Hi ebaines,
But the answer provided in the book is 6 hrs 53 minutes 20 seconds. Is that wrong?
• May 14th 2014, 04:52 PM
romsek
Re: Ambiguous Problem
Quote:

Originally Posted by Vinod
Hi ebaines,
But the answer provided in the book is 6 hrs 53 minutes 20 seconds. Is that wrong?

let $t_1=5$ and $t_2=3$

$4 t_1 + 5 t_2 = 4*5 + 5*3 = 35$

$5 t_1 + 4 t_2 = 5*5 + 4*3 = 37$

the total time spent walking is $t_1+t_2=8 hrs$

The book is incorrect, or you have not transcribed the problem correctly.
• May 15th 2014, 04:31 AM
ebaines
Re: Ambiguous Problem
You would get the answer provided by the book if the problem was changed slightly. If the girl walks 30 Km to the party, instead of 35 Km, and you leave the rest of the problem the same you get a total time of 6 hours, 53 minutes, 20 seconds.
• May 15th 2014, 05:00 PM
Vinod
Re: Ambiguous Problem
Hi ebaines,
Yes,you are correct.