SOLUTION: Please help me to solve this question!! : one third of a certain journey was covered at the speed of 20 km per hour , one fourth at the rate of 30 km per hour and the rest at th

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Question 1189258: Please help me to solve this question!!
: one third of a certain journey was covered at the speed of 20 km per hour , one fourth at the rate of 30 km per hour and the rest at the rate of 50 km per hour.
Find the average speed ( per hour ) of the whole journey ?
Found 3 solutions by josgarithmetic, Solver92311, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
1-1%2F3-1%2F4
12%2F12-4%2F12-3%2F12
5%2F12, the rest at 50 kilom per hr 

          SPEEDS      TIME                  DISTANCE

PART1        20       (d/3)(1/20)               d/3

PART2        30       (d/4)(1/30)               d/4

PART3        50       (5d/12)(1/50)             (5/12)d

SUM                                               d

total distance, d
total time, d%2F60%2Bd%2F120%2B%285d%29%2F600

AVERAGE SPEED, cross%281%2F%281%2F60%2B1%2F20%2B5%2F600%29%29
1%2F%281%2F60%2B1%2F120%2B5%2F600%29
-
1%2F%281%2F60%2B1%2F120%2B1%2F120%29
1%2F%281%2F60%2B2%2F120%29
1%2F%281%2F60%2B1%2F60%29
1%2F%282%2F60%29
1%2F%281%2F30%29
highlight_green%2830%29

Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the total time of the trip and represent the total distance traveled. The average speed is equal to



There are three parts of this trip, so let the three distances be represented by ,, and and we know that



Also, if we have accounted for one-third of the trip and one-fourth of the trip, the rest of the trip must amount to:









So


But the average speed is the total distance divided by the total time, , so:



You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
one third of a certain journey was covered at the speed of 20 km per hour ,
one fourth at the rate of 30 km per hour and the rest at the rate of 50 km per hour.
Find the average speed ( per hour ) of the whole journey ?
~~~~~~~~~~~~~~~~


            Calculations by @josgarithmetic have  FATAL  ERRORS,
            so I came to bring a correct solution. 


Let d be the distance.


Part d%2F3 was covered at 20 km/h;  it took  d%2F%283%2A20%29 = d%2F60 hours.

Part d%2F4 was covered at 30 km/h;  it took  d%2F%284%2A30%29 = d%2F120 hours.


The rest distance,  d+-+d%2F3+-+d%2F4 = %285d%29%2F12  kilometers, was covered at 50 km/h;  

                    it took %285d%29%2F%2812%2A50%29 = d%2F120 hours.


Total time is  d%2F60+%2B+d%2F120+%2B+d%2F120 = d%2F60+%2B+d%2F60 = 2d%2F60 = d%2F30.


Therefore, the average speed = d%2F%28%28d%2F30%29%29 = 30 km/h.    ANSWER.

Solved.


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