A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for 25.7 minutes at an average speed of 8.82 m/s. During the second part, she rides for 29.6 minutes at an average speed of 4.09 m/s. Finally, during the third part, she rides for 7.14 minutes at an average speed of 16.6 m/s. (a) How far has the bicyclist traveled during the entire trip? (b) What is the average speed of the bicyclist for the trip?

To find the distance the bicyclist has traveled during the entire trip, we can calculate the distance for each part and then sum them up.

For the first part, the distance can be found using the formula:
distance = speed × time

distance1 = 8.82 m/s × 25.7 minutes
= 8.82 m/s × (25.7 minutes × 60 seconds/minute)
= 8.82 m/s × 1542 seconds
≈ 13602.44 meters

Similarly, for the second part:
distance2 = 4.09 m/s × 29.6 minutes
= 4.09 m/s × (29.6 minutes × 60 seconds/minute)
= 4.09 m/s × 1776 seconds
≈ 7257.84 meters

And for the third part:
distance3 = 16.6 m/s × 7.14 minutes
= 16.6 m/s × (7.14 minutes × 60 seconds/minute)
= 16.6 m/s × 428.4 seconds
≈ 7106.64 meters

Now, to find the total distance:
total distance = distance1 + distance2 + distance3
≈ 13602.44 meters + 7257.84 meters + 7106.64 meters
≈ 27966.92 meters

Therefore, the bicyclist has traveled approximately 27966.92 meters during the entire trip.

To find the average speed of the bicyclist for the trip, we can use the formula:
average speed = total distance ÷ total time

First, we need to calculate the total time for the trip:
total time = time1 + time2 + time3
= 25.7 minutes + 29.6 minutes + 7.14 minutes
≈ 62.44 minutes

Now, let's convert the total time to seconds for convenience:
total time = 62.44 minutes × 60 seconds/minute
≈ 3746.4 seconds

Finally, we can find the average speed:
average speed = 27966.92 meters ÷ 3746.4 seconds
≈ 7.47 m/s

Therefore, the average speed of the bicyclist for the entire trip is approximately 7.47 m/s.

a) d = 60(25.7*8.82+29.6*4.09+7.14*4.09)

b) speed = d/[ 60(25.7+29.67.14) ]