Question

Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 4 meters per second. If the slower runner has a 75-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?

Answer 1

Answer:12.5 seconds

Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s

and Runner 2 with a speed of 4 m/s

the equation of displacement for a uniform movement is

x=V*t

so x1=V1*t

and x2=V2*t

and the problem condition is x2=x1+75m

so we proceed to solve the equations.

from equation 2 t=x2/V2

substituting in equation 1 we have

x1=V1(x2/V2) and then the 3 equation

x1=V1((x1+75m)/v2

finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m

then t=(x1/v1)=125/10=12.5 seconds

Answer 2

Answer:

12.5 seconds

Step-by-step explanation:

Speed of the first person = 10 meter per second

Speed of the second person = 4 meter per second

Relative velocity of faster person = 10 - 4 = 6 meter per second

since distance between both the person is = 75 meter.

Therefore, time to cover this distance by faster person = $\frac{Distance}{Speed}$

$\frac{75}{6}$

= 12.5 seconds.

Faster runner catches the slower runner after 12.5 seconds.