Question

Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip. What is the bicyclist's average speed in the air? What is the speed of the wind?

Answer 1

Answer:

The average speed of bicyclist is 120 miles per hours

The speed of wind is 30 miles per hours .

Step-by-step explanation:

Given as :

The distance that bicyclist cover = d = 30 miles

The time taken by bicyclist to cover 30 miles = t = 5 hours

Let the average speed of bicyclist = x miles per hours

Let The speed of wind = y miles per hours

Now, biking into wind

The time taken in return by bicyclist = 5 hours

∵ Speed = Distance × time

i.e  x + y = d × t

∴  x + y = 30 miles × 5 hours

Or, x + y = 150 mi/h          ...........A

Again

Now, biking against wind

The time taken in return by bicyclist = 3 hours

∵ Speed = Distance × time

i.e  x - y = d × t

∴  x - y = 30 miles × 3 hours

Or, x - y = 90 mi/h                  ......B

Solving equation A and B

(x + y) + (x - y) = 150 mi/h + 90 mi/h

Or, (x + x) + (y - y) = 240 mi/h

Or, 2 x + 0 = 240 mi/h

∴   x = $\dfrac{240}{2}$

i.e x = 120 mi/h

So,The average speed of bicyclist = x = 120 miles per hours

Now, Put the value of x into eq B

∵ x - y = 90 mi/h

Or,  120 mi/h  - y = 90 mi/h

∴ y = 120 mi/h - 90 mi/h  

I.e y = 30 mi/h

So,The  speed of wind = y = 30 miles per hours

Hence,The average speed of bicyclist is 120 miles per hours

And The speed of wind is 30 miles per hours .  Answer