Aman hiked a distance of 9 miles into the country. he rode back in a car along the same route at the rate of 27 mph. if the entire trip took 3 hours and 20 min, find his rate while walking.

The distance traveled by the man will be the product of its speed and the time taken in trip. Hence, by using this concept, we can calculate that the man took 0.33 hour in car to return, taking the same route and the man walked at a rate of 3 miles per hour in the trip.

Given information:

The distance hiked by the man is 9 miles.

The speed at which he rode back the car is 27 miles per hour.

The total time of the trip is 3 hour 20 min. which is equal to 3.33 hour.

Let, the time is the time he took to cover the distance in return,

So, according to the question,

Hence, the time he took to travel back is 0.33 hour.

As, the total time of the trip is 3.33 hour, so, the time taken to cover the distance of 9 miles which is hikes by the man will be the difference of total time taken in the trip and the time he took to rode back in the car.

Hence, the time taken by the man to walk 9 miles is 3 hour.

Now, the rate, at which he walked can be calculated as,

Hence, the man walked at a rate of 3 miles per hour in the trip.

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34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm