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A chauffeur drove 28 km, driving the first five minutes at full speed, the next five minutes at half speed, and the third five minutes at quarter speed. What is the full speed of the car?

 Apr 13, 2021
 #1
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+1

Call the speed s km per minute. 

 

Then in the first 5 minutes, 5s km are traveled. 
 

In the second 5 minutes, in half speed, we have s/2 km per minute, so 5s/2 km traveled. 

In the third 5 minutes, we have quarter speed, or s/4 km per minute 5s/4 km traveled. 

5s + 5s/2 + 5s/4 = 28 km total. 

5s + 5s/2 + 5s/4 = 35s/4

35s/4 = 28

s = 28*4/35 = 16/5

So the full speed is 16/5 km per minute or 192 km per hr

 Apr 13, 2021
edited by Guest  Apr 13, 2021
 #2
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+1

Let R  be  the  full speed....note  that 5 min   = (1/12) hr

 

And  rate  * time  =  disttance.....so.....

 

R(1/12)  + (R/2)(1/12)  +  (R/4)(1/12)  =   28

 

(1/12)  ( R  + R/2 + R/4)   =  28           multiply  both sides  by 12

 

(R  + R/2  + R/4)  =  336

 

( 4R  + 2R  + R)  / 4   =  336      multiply  both sides  by  4

 

7R   =    1344

 

R =  1344  / 7  =   192 km / hr

 

 

cool cool cool

 Apr 13, 2021

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