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?
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
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