Two cyclists are travelling at constant speeds around a 400 m track in opposite direction. The speed of Jeff is 1.5 times the speed of Rob. The cyclists find they meet every 20 s. What is the speed of Jeff?
A) 9.0 m/s
B) 12 m/s
C) 13 m/s
D) 20 m/s
E) 30 m/s
relative speed: 2.5xRobbspeed
they meet each cycle 20 sec
v=400/20=20m/s=relative speed.
but relative speed=Vrob+1.5Vrob
20m/s=2.5 Vrob
Vrob= 8m/s
VJeff=12m/s
To find the speed of Jeff, let's start by setting up equations for both cyclists.
Let's say Rob's speed is "x" m/s. Then Jeff's speed would be 1.5x m/s since Jeff's speed is 1.5 times the speed of Rob.
Now, let's analyze what is happening. The two cyclists are traveling in opposite directions around the 400 m track and meet every 20 s. This means that in 20 s, the combined distance they traveled would be equal to the circumference of the track, which is 400 m.
Since they are traveling in opposite directions, their combined speed would be the sum of their individual speeds. So, the combined speed of Rob and Jeff is (x + 1.5x) = 2.5x m/s.
We can now write the equation: distance = speed × time.
The distance covered by the combined speed in 20 s is 400 m. So, we have the equation: 400 = (2.5x) × 20.
To find the value of x, we can simplify the equation as follows:
400 = 50x
x = 400/50
x = 8
Therefore, Rob's speed is 8 m/s. Since Jeff's speed is 1.5 times Rob's speed, Jeff's speed would be 1.5 × 8 = 12 m/s.
So, the speed of Jeff is 12 m/s.
Therefore, the correct answer is B) 12 m/s.