A car going 60 miles per hour set out on a 400-mile trip at 12:00 P.M. Exactly 20 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 2:00 P.M.?
the first car went 20 miles before the 2nd car started out.
So, it made up 20mi/(5/3 hr) = 12 mi/hr
That is, car 2 was going 12 mi/hr faster than car 1, or 72 mi/hr
Check: car 1 went 120 miles in 2 hours
car 2 went 72(5/3) = 120 miles in 1 hr 40 min
To find the speed of the second car, we need to first determine the time it took for the second car to catch up with the first car.
The first car started the trip at 12:00 P.M. The second car started exactly 20 minutes later. Therefore, the second car started at 12:00 P.M. + 20 minutes = 12:20 P.M.
The first car traveled for 2 hours (from 12:00 P.M. to 2:00 P.M.) at a speed of 60 miles per hour. Thus, it covered a distance of 2 hours x 60 miles per hour = 120 miles.
Since the second car caught up with the first car, it must have traveled the same distance of 120 miles. The time it took for the second car to travel this distance can be calculated as follows:
Time = Distance / Speed
T = 120 miles / S miles per hour
The second car started at 12:20 P.M. and caught up with the first car at 2:00 P.M., which means it traveled for 2:00 P.M. - 12:20 P.M. = 1 hour and 40 minutes.
Converting 1 hour and 40 minutes to hours:
1 hour = 60 minutes, so 1 hour 40 minutes = 1 + (40/60) hours = 1.67 hours.
Therefore, we can set up the equation and solve for the speed (S) of the second car:
1.67 hours = 120 miles / S miles per hour
To find the speed of the second car (S), we can rearrange the equation:
S = 120 miles / 1.67 hours
Using a calculator, the speed of the second car is approximately:
S ≈ 71.86 miles per hour
Therefore, the second car was traveling at approximately 71.86 miles per hour.