Ted, a triathlete, can swim 1.2 miles in 25 minutes, bike 56 miles in 2 hours 25 minutes, and run 13.1 miles in 1 hour 35 minutes. He is training for an Olympic distance triathlon which is 0.9 mile swim, a 24.7 mile bike ride and a 6.2 mile run. If Ted completes each part of the race at the rates above, and passes the starting line at 9:03am, when should he expect to reach the finish line?

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9/12(25) + 24.7/56(145) + 6.2/13.1(95) = total time in minutes

Add total time to 9:03.

To determine when Ted should expect to reach the finish line, we need to calculate the total time it would take for him to complete each part of the race individually and then add them together.

Let's start by converting the time for each segment of the race to hours:

Swimming:
Ted swims 1.2 miles in 25 minutes, which is equivalent to 25/60 = 0.4167 hours.

Biking:
Ted bikes 56 miles in 2 hours 25 minutes, which is equivalent to 2.4167 hours.

Running:
Ted runs 13.1 miles in 1 hour 35 minutes, which is equivalent to 1.5833 hours.

Now, let's calculate the time it would take Ted to complete the Olympic distance triathlon:

Swimming:
Since the Olympic distance triathlon involves a 0.9 mile swim, Ted would take 0.4167 * (0.9 / 1.2) = 0.3125 hours.

Biking:
For the biking segment, Ted would take 2.4167 * (24.7 / 56) = 1.0621 hours.

Running:
For the running segment, Ted would take 1.5833 * (6.2 / 13.1) = 0.7491 hours.

Now, let's calculate the total time it would take Ted to complete the entire race:

Total time = Swimming time + Biking time + Running time
= 0.3125 + 1.0621 + 0.7491
= 2.1237 hours

Next, we need to add the total race time to the starting time of 9:03am to find out when Ted should expect to reach the finish line:

Finish time = Starting time + Total race time

To add the time, we need to convert the hours to minutes.

Total race time in minutes = 2.1237 * 60 = 127.42 minutes

Now, let's add the time to the starting time:

Finish time = 9:03am + 127.42 minutes

To convert the minutes to hours and minutes, we divide the minutes by 60 and add it to the hours, while keeping track of the carry-over.

Finish time hours = 9 + floor(127.42 / 60) = 11

Finish time minutes = (127.42 % 60) = 7.42, rounded to 7

Therefore, Ted should expect to reach the finish line at 11:07am.

11:10 am