Chapter 9.6, Problem 9P

To determine

To find: the total distance, time and speed of upstream and downstream flow.

Answer to Problem 9P

The total distance is $\text{1200km}$ ,total time taken is $\text{5}\text{.4h}$ and average speed is $\text{222}\text{.2}\text{km}/\text{h}$ .

Explanation of Solution

Given:

Flying with no wind a plane makes a $\text{600km}$ trip in $\text{3h}$ .

On the return trip the plane flies with a $\text{50}\text{km}/\text{h}$ wind.

Concept used:

Average speed= $\frac{\text{total distance}}{\text{total time}}$ or $\text{distance=speed}\times \text{time}$ .

  $\text{Time=}\frac{\text{distance}}{\text{speed}}$ .

Calculation:

The trip is $600$ km each way so the distances for both no wind and with wind are $600$ .

If the time to fly with no wind is $3$ hours, then the rate is $\frac{600}{3}$ $\text{=200}\text{km}/\text{h}$ .if the wind speed is $\text{50}\text{km}/\text{h}$ ,the rate with wind is $\text{200+50=250}\text{km}/\text{h}$ so it takes $\frac{\text{600}}{\text{250}}\text{=2}\text{.4 hours}$ .

	rate	time	distance
No wind	$\text{200}$	$3$	$\text{600}$
With wind	$\text{250}$	$2.4$	$\text{600}$

Total distance is then $\text{600+600=1200km}$ .

Total time is then $\text{3h+2}\text{.4h=5}\text{.4h}$ .

Average speed= $\frac{\text{total distance}}{\text{total time}}\text{=}\frac{\text{1200}}{5.4}\text{=222}\text{.2}\text{km}/\text{h}$ .

Hence, the total distance is $\text{1200km}$ ,total time taken is $\text{5}\text{.4h}$ and average speed is $\text{222}\text{.2}\text{km}/\text{h}$ .