An auto travels at a rate of 25 km/h for 4 minutes, then at 50 km/h for 8 minutes, and finally at 20 km/h for 2 minutes. Find the average speed for the complete trip in meters per second. (Give the answer to one decimal place accuracy.)

Sure, let's break this problem down into steps:

Step 1: Convert all speeds to the same unit The speeds are given in km/h, but the question asks for the answer in m/s. So, we need to convert the speeds from km/h to m/s. We know that 1 km = 1000 m and 1 hour = 3600 seconds. So, to convert km/h to m/s, we multiply by 1000 and divide by 3600.

25 km/h = 25 * 1000 / 3600 = 6.94 m/s 50 km/h = 50 * 1000 / 3600 = 13.89 m/s 20 km/h = 20 * 1000 / 3600 = 5.56 m/s

Step 2: Convert all times to the same unit The times are given in minutes, but we need them in seconds to match the unit of speed. We know that 1 minute = 60 seconds.

4 minutes = 4 * 60 = 240 seconds 8 minutes = 8 * 60 = 480 seconds 2 minutes = 2 * 60 = 120 seconds

Step 3: Calculate the total distance travelled The distance travelled at each speed is the speed times the time. So, we calculate the distance for each part of the trip and then add them up.

Distance at 25 km/h = 6.94 m/s * 240 s = 1665.6 m Distance at 50 km/h = 13.89 m/s * 480 s = 6662.4 m Distance at 20 km/h = 5.56 m/s * 120 s = 667.2 m

Total distance = 1665.6 m + 6662.4 m + 667.2 m = 8995.2 m

Step 4: Calculate the total time The total time is the sum of the times for each part of the trip.

Total time = 240 s + 480 s + 120 s = 840 s

Step 5: Calculate the average speed The average speed is the total distance divided by the total time.

Average speed = Total distance / Total time = 8995.2 m / 840 s = 10.7 m/s

So, the average speed for the complete trip is 10.7 m/s to one decimal place.