Chapter 4.8, Problem 2P

To determine

To calculate: the time of the jet & plane passing each other.

Answer to Problem 2P

Gracias overtook Smiths at 9:40 A.M.

Explanation of Solution

Given:

	$\text{speed}\times \text{time = Distance}$
Smiths	$?$	t	$?$
Gracias	$?$	$?$	$?$

Speed of Smiths = 48 mph

Speed of Gracias = 60 mph

Distance betweenAustin to los Angeles = 2100 kmph

Calculation:

Let the time taken by the Smiths = $x$

Let the time taken by the gracias = $x-\left(\frac{1}{3}\right)$

Speed of Smiths = 48 mph

Speed of Gracias = 60 mph

Distance covered by Smiths = $48\times x$ miles

Distance covered by jet = $60\times \left(x-\left(\frac{1}{3}\right)\right)$ miles

Now equating the distance covered by Smiths & Gracias

  $\begin{array}{l}48\times x=60\times \left(x-\left(\frac{1}{3}\right)\right)\\ 48x=60x-20\\ 12x=20\\ x=\frac{20}{12}\\ x=\frac{5}{3}\end{array}$

1 hrs 20 minutes

	$\text{speed}\times \text{time = Distance}$
Smiths	$48$	$\frac{5}{3}$	$80$ miles
Gracias	$60$	$\frac{4}{3}$	$80$ miles