Excluding stoppages the speed of a bus is 54km/hr and including stoppages it is 45km/hr. For how many minutes does the bus stop per hour.

Question

Excluding stoppages the speed of a bus is 54km/hr and including stoppages it is 45 km/hr. For how many minutes the bus stop per hour. 

Answer 1

This problem intended to help us understand units.

The commonly-used formula is called “D-I-R-T,”  for Distance-Is-Rate-times-Time.  With problems of this type, there will be two people or boats or trains or etc.  travelling the same distance or toward each other with a total distance given or at a slow and fast rate or etc.  – something that allows us to relate the D-I-R-T of one to the D-I-R-T of the other.  And, when we do, the units will be important.

This problem has one bus, no specific distance (so, we can set two distances equal and not have to know it), two rates and no specified time (it remains min/hr).  The problem asks us to find the difference in time per hour between a non-stop trip (an “express” bus) and a stopping-trip (a “local” bus).  Notice that km/hr is speed, but what is min/hr?  It is “stoppage,” “outage,” “set-up,” “shut-down,” “repair time,”  “vacation,” “sick time,” – you should be able to think of lots of problems that have these.

So, solving for R in D-I-R-T, R=D/T.
       R1 = 54 km/hr and R2 = 45 km/hr

To go the same distance D for the two busses:
       D = (speed of express bus)*(express time) = (speed of local bus)*(local time)
                     And we solve for wait time = local time – express time
       D = (54 km/hr)*(express time) = (45 km/hr)*(express time + wait time)
       D = 54*(express time) = 45*(express time + wait time)
              (54-45)*(express time) = 45*(wait time)
               (wait time) = (1/5)*(express time)

And, to include “stoppage” in terms of minutes per hour, 
                (wait time)/hr = (1/5)(express time)/hr
         So, per hour, the wait time is 12 min/hr.

Let’s check this using a trip of (conveniently) 54 kilometers:
      D = 54 km = (54 km/hr) * (1 hr) = (45 km/hr)*(1 hr + 12 minutes)
                 54 = (54/60)*60  = (45/60)*(72)                         (changed to minutes)
                       54 = 54      yes

Now that you know all this, you can start with:
              D = 54*1 = 45*(1+W)    and solve for W

Answer 2

David's answer has been voted best, but it cannot be right.

 

The bus travels 45 km every hour.    It is a simple matter to calculate how long it would take to cover this distance at 54 km/hr 

 

D = RT and T  = D/R.   45 Km / 54 KM/hr =  5/6 hour = 50 minutes.    The remaining time, 1/6 of an hour is stopping time.  That adds up to 10 minutes.

 

Muhammad C has the correct answer.

 

David correctly calculated that the train would stop for 12 minutes out of every 72, but the question asked how many minutes the bus would stop in 60 minutes.    12 out of 72 is the same as 10 out of 60.

Answer 3

This means bus travels at 54 mph when it is in motion. We just need to find how long it takes to travel 45 miles at 54 mph, and then we can reasonably say that the rest of the time within the hour is for stoppages.

 

54 miles/hour = 45 miles/x

 

x = 45/54 hours = 5/6 hour = 50 minutes

 

We can then say that the time left for stoppages would be 1 hour - 50 minutes which would be 10 minutes.