Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes more will it take him then if he travels the entire trip at 20 kilometers per hour?

Question

Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes more will it take him then if he travels the entire trip at 20 kilometers per hour?

Answer 1

total time at 20 km/h = 40 km/ 20 km/h

= 2 hours

time of 1st part = 10/30 = 1/3 hr = 20 minutes
time of 2nd part = 30/15 = 2hours
for a total of 2:20 hrs

so it would take him 20 minutes extra

Answer 2

To solve this problem, we need to find the total amount of time it takes for Phil to complete the trip at both speeds and then compare the difference.

First, let's calculate the time it takes for Phil to complete the trip using the given speeds:

For the first 10 kilometers at 30 kilometers per hour, Phil takes (10 kilometers) / (30 kilometers per hour) = 1/3 hour to complete.

For the remaining distance of the trip, which is 40 - 10 = 30 kilometers, Phil is traveling at 15 kilometers per hour. Therefore, he takes (30 kilometers) / (15 kilometers per hour) = 2 hours to complete.

So, the total time it takes for Phil to complete the trip is 1/3 hour + 2 hours = 7/3 hours.

Now, let's calculate the time it would take for Phil to complete the entire trip at a constant speed of 20 kilometers per hour:

The distance for the entire trip is 40 kilometers. At a speed of 20 kilometers per hour, Phil takes (40 kilometers) / (20 kilometers per hour) = 2 hours to complete the trip.

To find the difference in time, we subtract the time it takes at a constant speed of 20 kilometers per hour from the total time taken with varying speeds:

Difference in time = (7/3 hours) - (2 hours) = 1/3 hour

Now, we need to convert the difference in time from hours to minutes. Since there are 60 minutes in an hour, we multiply the difference in time by 60:

Difference in time in minutes = (1/3 hour) * (60 minutes per hour) = 20 minutes.

Therefore, it will take Phil 20 minutes more to complete the trip with varying speeds compared to traveling the entire trip at a constant speed of 20 kilometers per hour.