The difference between the digits of a two digit number is 1....

[mikkyjagga]

Hi ,can anybody help solve the following maths problems?

(1) The difference between the digits of a two digit number is 1.The number itself is 1 more than 5 times the sum of its digits.If the units digit is greater than the tens digits,find the number

(2) a man travels 10km in 50 minutes if he runs for 8km and walks for 2km.If he runs 4km and walks 6km,his time is 1h15min.Find his running and walking speeds.

 

[pka]

(1) The difference between the digits of a two digit number is 1.The number itself is 1 more than 5 times the sum of its digits.If the units digit is greater than the tens digits,find the number

\(\displaystyle \begin{align*} |d_1-d_0|&=1\\(10\cdot d_1 +d_0)-1&=5(d_1+d_0)\end{align*}\)

 

[Ishuda]

(1) The difference between the digits of a two digit number is 1.The number itself is 1 more than 5 times the sum of its digits.If the units digit is greater than the tens digits,find the number

\(\displaystyle \begin{align*} |d_1-d_0|&=1\\(10\cdot d_1 +d_2)-1&=5(d_1+d_0)\end{align*}\)

Make that
\(\displaystyle d_0\, -\, d_1\, =\, 1\)

 

[pka]

Make that
\(\displaystyle d_0\, -\, d_1\, =\, 1\)

In the number 65, the difference is in the digits in 1.

 

[Ishuda]

...(2) a man travels 10km in 50 minutes if he runs for 8km and walks for 2km.If he runs 4km and walks 6km,his time is 1h15min.Find his running and walking speeds.

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

HINT: Pay attention to your units. If you use something like
t_r1 + t_w1 = 50
s_r t_r1 = 2
s_w t_w1 = 8
where s_r is the running speed, t_r1 is the running time for the first travel, s_w is the walking speed, and t_w1 is the walking time for the first travel, then your speed will come out in km/min which you may need to convert to km/hr.

 

[Ishuda]

In the number 65, the difference is in the digits in 1.

Yes, but the problem said "the units digit is greater than the tens digits". BTW: My first question when looking at the problem initially was which difference - the first minus the second or the second minus the first. I then worked out for both and re-read the problem.

 

[lookagain]

\(\displaystyle \begin{align*} |d_1-d_0|&=1\\(10\cdot d_1 +d_2)-1&=5(d_1+d_0)\end{align*}\)

This is a good example of what I talked about speaking to the appropriate audience level.

Don't bring up absolute values in a elementary algebra problem such as this.

And your second equation isn't a direct translation of order from the English to algebra (regarding what is on either side of the equals sign)
for the immediate pair of equations.

Use two different letters so there isn't the needless complication with subscripts. "t" and "u," respectively, are standard.



Let t = the tens digit

Let u = the units digit

Then the number is 10t + u.


1st equation: u - t = 1


2nd equation: 10t + u = 1 + 5(t + u) \(\displaystyle \ \ \ \ \ \)

or

10t + u = 5(t + u) + 1

 

[mikkyjagga]

Re;the difference between digit numbers...

Hi,thank you all to those that responded to the above subject.I am very grateful.Lookagain did a good job with his simple solution.I realised that Denis did not change the time to hour .

 

[Deleted member 4993]

Denis/e is fractionally challenged!!!