Chapter 4.8, Problem 1OE

To determine

To fill: The table and write an equation for private plane and jet flying apart. Also, write the time at which they pass each other.

Answer to Problem 1OE

Equation for private plane and jet,

  $500t+700\left(t-1\right)=2100$

The private plane and jet flying apart pass each other at 2:20 PM.

Explanation of Solution

Given information:

Distance between Austin and Los Angeles is 2100 km.

Private plane left Austin for Los Angeles at 12 PM, flying at $500\text{km}/\text{h}$ .

Jet left Los Angeles for Austin on hour later, flying at $700\text{km}/\text{h}$ .

Since the private plane and jet are flying apart, the problem involves motion in opposite direction.

Let

t be the number of hours of the plane.

The jet left one hour after the plane.

Thus,

The jet flew for t − 1 hours.

Table represents the information according to the statement:

	Rate $\left(\text{km}/\text{h}\right)$	Time	Distance
Private plane	500	$t$	$500t$
Jet	700	$\left(t-1\right)$	$700\left(t-1\right)$

It is known that

Private plane and jet are moving in opposite directions towards each other.

Then

The combined distance traveled by both when they pass each other should be equal to the distance between the two cities.

It is also known

The private plane and jet started 2100 km apart.

The private plane flew 500t km.

And

The jet flew 700( t − 1) km.

Then

  $500t+700\left(t-1\right)=2100$

  

Now,

Solve the above equation:

  $500t+700\left(t-1\right)=2100$

That becomes

  $500t+700t-700=2100$

That further becomes

  $1200t=2800$

Divide both sides by 1200:

  $t=\frac{2800}{1200}=\frac{7}{3}=2\frac{1}{3}=\text{2}\text{hours}\text{20}\text{minutes}$

Thus,

The private plane and jet pass each other at 2:20 PM.