Final answer:
To calculate the time taken for each leg of the trip, we used the formula distance = speed × time and solved the set of equations. The boat spends 42 minutes going upstream and 36 minutes going downstream.
Step-by-step explanation:
To solve the problem regarding the average speed of a boat traveling upstream and downstream, we must use the concept of rate, time, and distance. The boat travels at 30 miles per hour upstream and at 35 miles per hour downstream. The total trip time is given as 1 hour and 18 minutes, which is equivalent to 1.3 hours (since 18 minutes is 0.3 of an hour).
Let's denote the time taken to travel upstream as t hours and downstream as 1.3 - t hours. We also know that the distance traveled upstream and downstream is the same, which allows us to set up two equations based on the formula distance = speed × time.
Upstream: Distance = 30 miles per hour × t hours
Downstream: Distance = 35 miles per hour × (1.3 - t) hours
Because the distances are equal:
30t = 35(1.3 - t)
Solving for t, we get:
30t = 45.5 - 35t
65t = 45.5
t = 45.5 / 65
t = 0.7 hours (or 42 minutes)
Therefore, the time taken to travel upstream is 42 minutes and to travel downstream is 1.3 hours - 0.7 hours = 0.6 hours, or 36 minutes.