At a certain time, Janice notices that her digital watch reads (a) minutes after two o'clock. Fifteen minutes later, it reads (b) minutes after three o'clock. She is amused to note that (a) is six times greater than (b). What time was it when she looked at her watch for the second time?
Please help in any way you can! Thanks! :-)
I see no one has answered so let me give you my thoughts. First, I think you can logically deduce the answer. If a =6*b and the difference between a and b is 15 minutes,(and since adding 15 minutes to the 2:00 + a time moves PAST the hour to give 3:00+ b time) then b must be sometime between 46 minutes and the hour; therefore, anything more than 10 minutes for a won't work because that will be over 60 minutes. 9 minutes for b would make 9*6=54 and 2:54 + 15 minutes =2:69 or 3:09. Works perfectly.
8 minutes after the hour would fit into the 15 minutes before the previous hour but 2:48 + :15 = 3:03 doesn't get 3:08. And anything less than 8 (1 min through 7 minutes) doesn't give a number which will add to over the hour in 15 minutes. So 8 and 9 minutes are the only possibilities and 8 doesn't work.
I tried a + 15 = 60+b and a=6*b for the equations.
That gives me a=45+b and 6b=45+b; then
5b = 45 and b = 9 so 3:00 + b minutes = 3:09, the time Jane looked at her watch the second time.
To solve this problem, we can set up a system of equations using the given information.
Let's assume that a represents the number of minutes after two o'clock when Janice looked at her watch for the first time, and b represents the number of minutes after three o'clock when she looked at her watch for the second time.
Based on the given information, we know that a = 60 + b, since one hour (60 minutes) separates two o'clock from three o'clock.
We're also told that a is six times greater than b, so we can write this as a = 6b.
Now we can solve the system of equations to find the values of a and b.
Substitute the expression for a from the second equation into the first equation:
6b = 60 + b
Simplify the equation:
6b - b = 60
Combine like terms:
5b = 60
Divide both sides by 5:
b = 12
We have found that b = 12, which represents the number of minutes after three o'clock when Janice looked at her watch for the second time.
To find the time when Janice looked at her watch for the second time, we add b minutes to three o'clock:
3:00 + 12 minutes = 3:12
Therefore, it was 3:12 when Janice looked at her watch for the second time.
yeah...
i don't know about that equation though.
i don't think 15 fits into it....
LOONDSI
i tried this one. kinda.
i don't think this is right but my equation was this:
6a+15=b
-15 -15
6a=b-15
-b -b
-15=6a-b
-1(-15=6a-b)
15=(-6)a+b
and then i guessed and checked...
(-2,3) worked but that didn't help. now i'm stuck too.
nooni
maybe it's
6a=b? and they are 15 min apart?
Okay... I think the thing we need to do is find another equation then try the elimination method.
But what would be another equation? Hmm... :-)
Would it (possibly) be a - 15 = b, because 15 mins later, it was (b) minutes after three o'clock?