Lesson Advanced arithmetic word problems on Travel & Distance

Advanced arithmetic word problems on Travel & Distance

Problem 1

The trip in residential area is 1/4 of 20 miles, i.e. 5  miles.


The time spent on residential area is   =  of an hour.


The time remaining to drive on freeway is   = -  =  =  of an hour,

where the fraction 25/60 represents 25 minutes, or 25/60 of an hour.



The trip on the freeway is 3/4 of 20 miles, or  15 miles long.

So the speed on the freeway should be   = 4*15 = 60 miles per hour.


ANSWER.  The speed on freeway should be 60 miles per hour.

Problem 2

From the problem, we may think that John and Lester started simultaneously from the "passing" point,
which is 15 km from the end.


From the problem, we see that Lester spent 45 minutes (or 3/4 of an hour) to cycle 9 kilometers.


Hence, the Lester' speed is   = 12 kilometers per hour.


Cycling with the speed of 12 km/h, Lester spent   =   hours, or 75 minutes, to cover 15 kilometers.


From the problem, John spent 45 minutes less than Lester, i.e. 75-45 = 30 minutes, or 1/2 of an hour.


                                 distance of 15 km
Thus we find the John' speed  = ------------------- = 15/(1/2) = 30 kilometers per hour.
                                 time 30 minutes


At this point, the problem is completely solved.


ANSWER.  John' speed was 30 kilometers per hour.

Problem 3

In the first scenario, Mary and Murray travel 3 hours toward each other.  

Hence, their approaching rate is  240/3 = 80 kilometers per hour.


In the second scenario, Murray moves alone during 2 hours from 8 am to 10 am,
and after that, they move 2.5 hours together toward each other.

In these 2.5 hours, the distance between them decreases by 2.5*80 = 200 kilometers.


It means that the distance which Murray travels alone in 2 hours from 8:00 am  to  10:am  is 

        240-200 = 40 kilometers .


Hence, the Murray' speed is 40/2 = 20 km/h.


Then the Mary' speed is 80-20 = 60 km/h.


ANSWER.  Mary' speed is 60 km/h;  Murray' speed is 20 km/h.