# How many minutes is it until 5:00 if forty minutes ago it was four times as many minutes past 2 o'clock?

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Let the minutes till 5 be x

==> the time is 5:00 - x minutes

==> the time forty minutes ago was: (5:00- x) - 40 ..........(1)

Given the the time forty minutes ago was 4 times as many minutes past 2 ocklock

==> 2 : 00 + 4x ............(2)

The time (1) = time (2):

==> (5:00 - x ) - 40 = 2:00 + 4x

==> 5:00 - 40 - 2:00 = 4x + x

==> 3:00 - 40 = 5x

==> 2:20 = 5x

==> 2 h = 120 min

==> 140 = 5x

==> x = 140/5 = 28m

**Then the time is 28 min till 5:00 **

**-==> 5:00 - 28 m = 4: 32**

**The time now is 4: 32**

We have to determine the present time first before finding how many minutes it is until 5:00.

Let the present time be x in hour.

The minutes till 5.00 = (5-x)60

Then 40 minutes ago the time was 60x-40minutes,

So the time 60x-40 minutes is past 2 :00 by 60x-40-120 = 60x-160.

Therefore (5-x) 60 = 4 (60x - 160).

300-60x = 240x -640

300+640 = (240+60)x

940 = 300x

x = 940/300.

x = 94/30

x = 188/60 = 3:08 time in hr : minutes frmat.

Therefore 5:00 -3:08 = 112 minutes is the minutes till 5:00.

Tally:

Untill 5 oclock the from 3.08 = 112 minutes.

$0 minutes ago the time = 3:08-0:40 = 2:28.

2:28 is 28 minutes past 2:00.

4 imes 0:28 = 112 minutes.

To solve this question it is best to represent all times in minutes.

Thus the time h:m = 60*h + m minutes

Where:

h = hours and m = minutes

Then:

5:00 = 5*60 = 300 minute

2:00 = 2*60 = 120 minutes

Let the present time be x minutes

Then:

Number of minutes until 5:00 = 300 - x

And Number of minutes until 5:00, 40 minutes ago = 300 - x + 40 = 340 - x

And number of minutes past 2:00 at present

= x - 120

It is given that:

Minutes past 2:00 at present

= 4(Number of minutes until 5:00, 40 minutes ago)

==> x - 120 = 4(340 - x)

==> x - 120 = 1360 - 4x

5x = 1480

x = 296 minutes

Converting x in h:m format

Present time = 04:56

Therefore:

Time in minutes until 05:00 = (05:00) - (04:56) = 4 minutes