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QuestionTiffany trains for a triathlon: 2.4-mile swim at 1.2mph1.2 \mathrm{mph}, 112-mile bike at 17.8mph17.8 \mathrm{mph}, and 26.2-mile run at 6.2mph6.2 \mathrm{mph}. Estimate total time.

Studdy Solution

STEP 1

Assumptions1. The swim distance is.4 miles. The bike ride distance is112 miles3. The run distance is26. miles4. Tiffany's average swim speed is1. mph5. Tiffany's average bike speed is17.8 mph6. Tiffany's average run speed is6. mph7. Tiffany maintains her average speeds throughout each leg of the triathlon

STEP 2

First, we need to find the time it takes for each leg of the triathlon. We can do this by dividing the distance by the speed for each leg.
Time=DistanceSpeedTime = \frac{Distance}{Speed}

STEP 3

Now, plug in the given values for the swim distance and swim speed to calculate the swim time.
Swim time=2. miles1.2 mphSwim\, time = \frac{2.\, miles}{1.2\, mph}

STEP 4

Calculate the swim time.
Swim time=2.4 miles1.2 mph=2 hoursSwim\, time = \frac{2.4\, miles}{1.2\, mph} =2\, hours

STEP 5

Next, plug in the given values for the bike distance and bike speed to calculate the bike time.
Bike time=112 miles17.8 mphBike\, time = \frac{112\, miles}{17.8\, mph}

STEP 6

Calculate the bike time.
Bike time=112 miles17.8 mph≈6.29 hoursBike\, time = \frac{112\, miles}{17.8\, mph} \approx6.29\, hours

STEP 7

Finally, plug in the given values for the run distance and run speed to calculate the run time.
Run time=26.2 miles6.2 mphRun\, time = \frac{26.2\, miles}{6.2\, mph}

STEP 8

Calculate the run time.
Run time=26.2 miles6.2 mph≈4.23 hoursRun\, time = \frac{26.2\, miles}{6.2\, mph} \approx4.23\, hours

STEP 9

Now that we have the time for each leg of the triathlon, we can find the total time it will take Tiffany to complete the triathlon. This is the sum of the swim time, bike time, and run time.
Total time=Swim time+Bike time+Run timeTotal\, time = Swim\, time + Bike\, time + Run\, time

STEP 10

Plug in the values for the swim time, bike time, and run time to calculate the total time.
Total time=2 hours+6.29 hours+4.23 hoursTotal\, time =2\, hours +6.29\, hours +4.23\, hours

STEP 11

Calculate the total time.
Total time= hours+6.29 hours+4.23 hours=.52 hoursTotal\, time =\, hours +6.29\, hours +4.23\, hours =.52\, hoursIt will take Tiffany approximately.52 hours to complete the triathlon.

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