Derek runs onto an escalator to the second floor, but the escalator is
moving downward. He runs 3 steps for each second. 30 seconds after he steps
on the escalator, Kenny runs onto this escalator with 4 steps per second.
The moving speed of the escalator is 1.5 steps/sec, and it has 150 steps.
How many steps are left when Kenny catches up Derek? Round your answer to
the nearest whole number.
The moving speed of the escalator is 1.5 steps/sec
He (Derek) runs 3 steps for each second.
If the escalator were stopped, Derek would be running 3 steps/second, but
the escalator slows him down by its speed, so his speed is
3-1.5=1.5 steps/second.
30 seconds after he (Derek) steps on the escalator...
At this instant, using d=rt, Derek is 30(1.5)=45 steps up the escalator
...Kenny runs onto this escalator with 4 steps per second.
If the escalator were stopped, Kenny would be running 4 steps/second, but
the escalator slows him down, so his speed is 4-1.5=2.5 steps/second.
Kenny's approach rate to Derek is the difference of their speeds which is
(2.5)-(1.5)=1 step/second.
How many steps left when Kenny catches up Derek?
Using t=d/r, since they are 45 steps apart, Kenny catches Derek in
45/1=45 seconds. At that instant, using d=rt, Kenney has traveled
(2.5)(45) = 112.5 steps up the escalator, so there are 150-112.5=37.5 steps
left.
Round your answer to the nearest whole number.
We round up to 113 steps.
Edwin