Question

(URGENT) Gertrude and Russell are traveling on their motor scooters in the same direction along the same road. Gertrude is traveling at 10 mph and is exactly 3 miles ahead of Russell, who is traveling at 14 mph. How many hours will it take Russell to catch Gertrude? (Write your answer as a decimal.)

Answer 1

Answer:

It will take 0.75 hours to Russell catch Gertrude

Step-by-step explanation:

Cinematics

The equations of cinematics include velocity, displacement and time. In case only the magnitudes are important, we can use the concepts of speed and distance. The speed can be thought in relative terms, i.e. if one body moves at 10 m/s and other moves at 8 m/s, we can say the relative speed is 2 m/s.

The equation who relates those magnitudes is

$x=vt$

The problem states Gertrude travels at 10 mph and is 3 miles ahead of Russell who travels at 14 mph. We want to know the time when Russell will catch Gertrude. Since Russell goes faster than Gertrude, he eventually catches her. In a time t, he must travel 3 miles more than her. Since the relative speed of them is 14-10= 4 mph, we can know the time it takes to the encounter to produce

$\displaystyle t=\frac{x}{v}$

$\displaystyle t=\frac{3}{4}=0.75\ hours$

Answer: It will take 0.75 hours to Russell catch Gertrude