Question

At 10 A.M. a plane leaves Boston, Massachusetts, for Seattle, Washington, a distance of 3000 mi. One hour later a plane leaves Seattle for Boston. Both planes are traveling at a speed of 300 mph. How many hours after the plane leaves Seattle will the planes pass each other?

Answer 1

Answer:

The plane from Seattle will pass the plane from Boston after 4.5 hours of its departure from the Seattle.

Step-by-step explanation:

Plane-1 = Boston, Massachusetts - Seattle, Washington at 10:00 AM

Plane-2= Seattle, Washington - Boston, Massachusetts at 11:00 AM

Speed of plane-1 = 300 mile/hour

Distance covered by plane-1 in 1 hour = 300 mile/h × 1 h = 300 mile

Distance between plane-1 and plane 2 after 1 hour :

= 3000 mile - 300 mile = 2700 mile

Let the distance covered by plane-1 after 1 hour be x in t time where it will pass plane-2.

Let the distance covered by plane-2 be y in t time where it will pass plane-1.

x + y = 2700 ...[1]

Speed of plane-1 = 300 mile/hour

$300 mile/h=\frac{x}{t}$..[2]

Speed of plane-2 = 300 mile/hour

$300 mile/h=\frac{y}{t}$..[3]

Putting value of t from [2] in [3];

$t=\frac{x}{300 mile/h}$

$300 mile/h=\frac{y}{\frac{x}{300 mile/h}}$

$\frac{x}{300 mile/h}=\frac{y}{300 mile/h}$

x = y

In [1] put x = y

y + y = 2700 miles

2y = 2700 miles

y = 1,350 mile

For the value of t, put the value of y in [3]:

$t=\frac{1,350 mile}{300 mile/h}=4.5 hour$

The plane from Seattle will pass the plane from Boston after 4.5 hours of its departure from the Seattle.