Question

I need to know how to set this problem up. On monday a security guard spent 4.5hours on patrol and 2hours on surveillance.On tuesday the officer spent 1 hour and 40 minutes on surveillance and 3 hours on patrol. Which day has a greater ratio of time on surveillance to time on patrol. some one said 7hours ans 30min on patrol and 40min on surveillance???

Answer 1

OK.......

So, 
ON MONDAY:
Time spent on patrol = 4.5 hrs
Time spent on surveillance = 2 hrs

ON TUESDAY:
Time spent on patrol = 3 hrs
Time spent on surveillance = 1 hr 40 min

Now,
The question is asking us the ratio of surveillance to patrol so, the value of surveillance needs to be on the top.

So,
Let's first change all the units to common units.....i.e. either hrs. to minutes or minutes to hrs.

In this case  .....i think it will be easier to convert minutes to hrs.. because if we do that ...we only have to do one conversion.

So,
1 hr. 40 minuter = 1hr + (40 /60) hrs
                        = 1 + 0.67 
                        = 1.67 hrs

So,
ON TUESDAY:
Time spent on surveillance  = 1.67 hrs

Now,
Let us find the ratio of surveillance to patrol on both days:

ON MONDAY:
Ratio of surveillance to patrol = $\frac{2}{4.5}=.44444444444$

ON TUESDAY:
Ratio of surveillance to patrol = $\frac{1.67}{3}=.556666667$

Now,
If we look at the ratio, the ratio of TUESDAY sure is greater than ratio on MONDAY

So, Tuesday has a greater ratio of time on surveillance to time on patrol