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:12.5 secondsStep-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*tso x1=V1*tand x2=V2*tand the problem condition is x2=x1+75mso we proceed to solve the equations.from equation 2 t=x2/V2substituting in equation 1 we havex1=V1(x2/V2) and then the 3 equationx1=V1((x1+75m)/v2finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125mthen t=(x1/v1)=125/10=12.5 seconds