) Two athletes, A and B, set off from the same point, but in opposite directions, at constant
speed around a track of circumference 400 m. If they meet again after 50 s, and the speed of
A is 1.5 times that of B, calculate the speed of each
THIS IS NOT DETAILED
To find the speed of each athlete, we can set up a system of equations using the information given.
Let's denote the speed of athlete B as v (in meters per second). According to the problem, the speed of athlete A is 1.5 times that of athlete B, so the speed of athlete A can be represented as 1.5v.
The distance traveled by each athlete can be determined using the formula: distance = speed × time.
The time taken by both athletes to meet again is 50 seconds. Since they start from the same point and go in opposite directions, their combined distance covered should equal the circumference of the track, which is 400 meters.
Now we can write the equations:
Distance covered by athlete A = speed of A × time = (1.5v) × 50 = 75v meters
Distance covered by athlete B = speed of B × time = v × 50 = 50v meters
Since they meet again after 50 seconds, the sum of the distances covered by both athletes should be 400 meters:
Distance covered by A + Distance covered by B = 75v + 50v = 400 meters
Combining like terms:
125v = 400
Solving for v:
v = 400 / 125 = 3.2 m/s
Now we can substitute the value of v back into the equation to find the speed of athlete A:
Speed of A = 1.5v = 1.5 × 3.2 = 4.8 m/s
Therefore, the speed of athlete A is 4.8 m/s, and the speed of athlete B is 3.2 m/s.
Together, their speed is 400m/50s = 8 m/s
A's speed is 3/5 of that, or 4.8 m/s
B's speed is 2/5, or 3.2 m/s