leanmeamum wrote:

a) the first clock

needs to gain 18 X 60 secs to show correct time

18 X 60 = 1080 seconds

7.5 secs gained in = 1 hour

so 1080 / 7.5 = 144 hours or 6 days needed to show correct time

write this as

18 x 60

---------

7.5

and it can cancel to

18 x 8

which is probably simpler than trying to divide by 1080 by 7.5

leanmeamum wrote:

b) clock 2

11.25 secs lost = 1 hour

30 X 60 = 1800 secs to lose

1800 / 11.25 = 160 hours or 6 days 16 hours

so 16 hours extra than required time to coincide with clock 1

11.25 X 16 = 180 seconds

So second clock will be 180 seconds or 3 minutes fast when the first clock shows the right time

Or you could write it as the number of seconds this one will lose in the time the first one is gaining - i.e. seconds per hour x number of hours / seconds in a minute

(converting 11.25 back to a fraction)

45 x 144 hours / 60

---

4

or

45 x 144

----------

4 x 60

which simply cancels down to

3 x 9

which you can subtract from 30 to give 3.