Question

Train A leaves New York for California at the same time Train B leaves California for New York. They are 2900 miles apart. They both travel at an average speed of 120 mph. A. What is the velocity of train A? B. What is the velocity of train B? C. How long will it take before they meet? Show your work.

Answer 1

Answer:

(A) 120 mph

(B) -120 mph

(C) 12 hours 5 minutes.

Step-by-step explanation:

Given that,

New York and California are 2900 miles apart,

Both the trains A as well as B travel at an average speed of 120 mph.

Assuming that the path between the starting point in New York and the ending point in California is straight, so the given distance of 2900 miles is actually the shortest distance which is the displacement between the source and destination.

So, the given speed on the straight path is actually the velocity.

Assuming that the velocity is positive in the direction from New York towards California.

(A) So, the velocity of train A (towards California)  = 120 mph.

(B) The velocity of train B (towards New York) = -120 mph.

(C) Bothy are moving towards each other, so the relative velocity between them is 120+120=240 mph, and the initial distance between them is 2900 miles.

When they meet, the displacement between them becomes zero, displacement covered= 2900-0=2900 miles.

So, the time, t, taken to cover the displacement 2900 miles with a relative velocity of 240 mph is

$t=\frac{2900}{240}$ [as time= displacement / relative velocity]

$\Rightarrow t=12\frac{1}{12}$ hours

=12 hours 5 minutes.