Chapter 9.6, Problem 14P

To determine

Tofind:The total flying time for the round trip if there is no wind.

Answer to Problem 14P

The total time would be $\frac{1200}{500}=2.4$ hours.

Explanation of Solution

Given:

It takes an airplane $\text{1h 30min}$ to fly $\text{600}$ km against the wind.

The return it takes only $\text{1}$ hours.

Concept used:

  $\text{Distance=rate}\times \text{time}$ .

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

Let $\text{r}$ be the rate of plane without wind and $\text{w}$ be the rate of the wind.

Then the plane’s rate with the wind is $\text{r+w}$ and against the wind is $\text{r-w}$ .

Using formula:

  $\text{distance=rate×time}$ .

  $\text{600=}\left(\text{r+w}\right)\left(1\right)$ .

Dividing both side by $\text{60}$ :

  $\text{r+w}=600$ ………………. $\left(\text{i}\right)$

Similarly,

  $\text{600=}\left(\text{r-w}\right)\left(1.5\right)$ .

  $\text{r-w}=400$ ……………….. $\left(\text{ii}\right)$

Adding the equation $\left(\text{i}\right)$ and $\left(\text{ii}\right)$

  $\text{r=500}$ .

The total distance of the flight is then $\text{2}\left(\text{600}\right)\text{=1200km}$ so at the rate of $\text{500}\text{km}/\text{h}$ ,the total time would be $\frac{1200}{500}=2.4$ hours.

Hence, the total time would be $\frac{1200}{500}=2.4$ hours.