Tracy drives from San Antonio to Montero a distance of 1975

Tracy drives from San Antonio to Montero, a distance of 197.5 miles. She starts driving at a constant speed and reduces her speed by 5 mph after each half hour of driving. If the trip takes 3 hr 20 min, how far did he travel in the first 2 hours?

Solution

Let Tracy\'s initial speed be x mph. Since tracy reduces speed by 5 mph every half hour and since the journey of 197.5 miles from San Antonio to Montero, takes 3hours and 20 minutes, the spped is reduced 6 times. The speed isas under for the 6 intervals of half an hour each:

1st -- X

2nd-- (x -5)

3rd-- (x -10)

4th-- ( x -15)

5th-- ( x - 20)

6th (x -25).

Now, there are another 20 minutes ( 20/60 hrs) left duting which the speed will remain x -25 mph.

Since distance = speed x time, we have the following equation:

x * 1/2 + (x - 5)* 1/2 + ( x -10)*1/2 + (x -15)*1/2 + (x -20) *1/2 + (x -25)* 1/2 + (x -25)*20/60 = 197.5

On simplifying, we have 1/2 (6x) + 1/3 x - 1/2 (5 + 10 + 15 + 20 +25) - 25 *1/3 = 197.5 or, 3x+ (1/3) x - 75/2 -25/3 = 197.5 or, (10/3)x = 197.5 + 75/2 + 25/3 = 395/2 +  75/2 + 25/3 = 470/2 + 25/3 = 1460/6 = 730/3. Therefore, x = 730/10 = 73.

In 2 hours, tracy travelled x * 1/2 + (x - 5)* 1/2 + ( x -10)*1/2 + (x -15)*1/2 = 1/ 2 (4x) -1/2( 5 + 10 + 15) = 2x - 15 = 2 *73 - 15 = 146 - 15 = 131 miles.