You and your friend are in a canoe race. Your friend is a half mile in front of you and paddling 3 miles per hour. You are paddling 3.4 miles per hour.

a. You are 8.5 miles from the finish line. How long will it take you to catch up to your friend?

b. You both maintain your paddling rates for the remainder of the race. How far ahead of your friend will you be when you cross the finish line?

Let the time that you caught up with your friend be t, then

8.5 - 3.4t = 8 - 3t

3.4t - 3t = 8.5 - 8

0.4t = 0.5

t = 0.5/0.4 = 1.25

therefore, you will catch up with your friend after 1.25 hours.

b.) time it will take you to cross the finnish line = 8.5/3.4 = 2.5 hours

After 2.5 hours, distance covered by your friend = 3 x 2.5 = 7.5 miles

Therefore, when you cross the finish line, you are 8 - 7.5 = 0.5 miles ahead of your friend.

A. in one hour, you will reduce the distance for 3.4 - 3 = 0.4 miles

which means you can catch up 0.1 miles for every 15 minutes

The amount of time before you catch up would be : 1 hour + 15 minutes

B. after catching up, there is only 8 miles distance remain

to achieve 8 miles, you need 8 / 3.4 = 2.35 hours

Distance created = 2.35 x 0.4

= + / - 0.94 miles