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

The average speed of the cyclist in the air is 8 miles per hour, and the speed of the wind is -22 mph.

Step-by-step explanation:

To find the average speed of the cyclist, we need to calculate the total distance traveled and the total time taken. The cyclist takes 5 hours to travel 30 miles against the wind, which means their speed is 30 miles/5 hours = 6 miles per hour. On the return trip, the cyclist takes 3 hours to cover the same 30 miles with the wind. So their speed is 30 miles/3 hours = 10 miles per hour. The average speed of the cyclist is the average of these two speeds, which is (6 mph + 10 mph) / 2 = 8 miles per hour.

To find the speed of the wind, we need to find the difference between the speed of the cyclist and the speed of the wind when they are biking against the wind and with the wind. When biking against the wind, the cyclist's speed relative to the air is the sum of the cyclist's speed and the wind speed, so the wind speed is 6 mph - 30 mph = -24 mph. Since the wind is blowing against the cyclist, the wind speed is negative. When biking with the wind, the cyclist's speed relative to the air is the difference between the cyclist's speed and the wind speed, so the wind speed is 10 mph - 30 mph = -20 mph. The average speed of the wind is the average of these two wind speeds, which is (-24 mph + -20 mph) / 2 = -22 mph.

Answer 2

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 =
`(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