Until 1883, every city and town in the united states kept its own local time. today, travelers reset their watches only when the time change equals 1.0 h. how far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by 1.0 h? (hint: earth rotates 360° in about 24 h.)

the length that must be traveled to change the time in 1 h  is 22 10⁶ m  

Explanation:

We can work the exercise a rule of three or rule of proportions. The earth rotates 360º in 24 hours when it rotates in 1 hour

      θ = 360 * 1/24

      θ = 15º

This means that every 15th time must be changed in 1 h

With this we can calculate the average distance, we take as data the average radius of the Earth that is 6.37 * 106 m, in the first approximation the planet is considered a sphere, so the length on its surface is 2πR, this calculation is only accurate in the equator, in the case of being in the tropics, the radius of the ring must be calculated at this latitude. We calculate the total length

       L = 2πR = 2 π 6.37 106

       L = 40 106 m

We write another rule of proportions if the total length is in 360º that length (L1) is in 15º

       L1 = L 15/360

       L1 = 40 10⁶ 15/660

       L1 = 1.67 10⁶ m

This is the length that must be traveled to change the time in 1 h

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y