Solve each problem. See Example 2. At the 2008 Summer Olympics in...

Question

Solve each problem. See Example 2. At the 2008 Summer Olympics in Beijing, Usain Bolt set a new Olympic and world record in the 100-m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? How would this time compare to the fastest time for a marathon, which is 2 hr, 3 min, 23 sec, set in 2013? (Hint: 1 m ≈ 3.281 ft.) (Data from Sports Illustrated Almanac.)

Accepted Answer

Hey, everyone in this problem, an active participant can walk a distance of 50 m in just 59.8 seconds. If they want to attend a walk for a cause, calculate the time required To finish a 34 mile walk, they keep the same pace in their walking. We're given four answer choices. Option a 18 hours, 10 minutes and 42 seconds. Option B 18 hours, 10 minutes and 50 seconds. Option C 18 hours one minute and seconds. And option D 18 hours, 10 minutes and nine seconds. Now, we're trying to figure out the time required and for this participant to finish a 34 mile walk, ok. So we call that we can calculate the time, ok? Using the distance and the speed, the time is going to be equal to the distance traveled divided by the speed that you're traveling at. Now, we know the distance we're given that the distance is 34 miles. We don't know the speed, ok. So in order to calculate the time required, we need to figure out the speed. Now, we're told that they keep the same pace as in their walking And they can walk 50 m in 59.8 seconds. So let's use that information to figure out their speed. Ok. So we can write this equation, we have times equal the distance over speed, we can rewrite it, ok? To find the speed, the speed is equal to the distance traveled divided by the amount of time it takes. Now the participants walk, they can walk 50 m. So the distance is 50 m and it takes 59. seconds. So we're gonna divide by 59.8 seconds and we get a speed of this participant of approximately 0. meters per second. So now we have the participants speed, ok? We also know their distance so we can calculate the time. Now we have to be a little bit careful here. The speed we have is in meters per second, but the distance we're given is in miles. So let's go ahead and convert our 34 miles into meters so that we have a consistent units and then we can get back to that equation. So our 34 miles, It's going to be equal to 34 miles Multiplied by 1609.34, 4 m per mild. Ok. So the unit of mile will divide out. Now We're left with 34 multiplied by 1609.344, Which gives us 54,717. m. So we have our speed in meters per second. We have our distance in meters. We can go ahead and use that first equation we wrote down to calculate the time. So the time taken again is going to be equal to the distance divided by the speed. OK? So this is equal to 54,717. m divided by The speed. 0.83, 12 m/s. Yeah, when you have a word problem like this, you can always use your units to double check the equations you have. OK? We have meters divided by meters per second. The unit of meters divides out. We're left with a unit of second in the numerator, which is the unit for time. OK? So our units do work out here. So if you ever get mixed up on what, which um value you should be dividing by which one you should, should be in the numerator. You can always use your units to double check. Now, when we work this out, We're gonna get 0.4 seconds. Now, that's the time we have, that's the what we were looking for. OK. The time required to finish that 34 miles. But if we remember our answer choices they're given in hours, minutes and seconds. OK? We have just seconds. So we need to take this time we found and break it out into hours. Minutes and seconds. So let's start With our 0.4 seconds. Ok? We're gonna divide this by 60 seconds per minute. And what this is gonna leave us with is it's gonna leave us with 0.7066. The unit of seconds divides out and we're left with a unit of minutes. Ok. So now we've converted completely to minutes. Also, not what we want to do, but we're gonna work up to the hours. So we're gonna divide this again by 60 minutes per hour Again. The unit of minute cancels. We're left with the unit of hour and we get .17, 8, 4, 4 hours. Now, this is a little bit confusing. How do we convert this 0.17844 to minutes and seconds? Let's just start with hours. Ok. We know that we have 18 full hours. So our hours is gonna be 18. If we consider that we have 18 hours, We know that there are 60 minutes per hour And we know that there are 60 seconds per minute. OK. So 18 hours is gonna be equal to 64, And 800 seconds. Now, we know our participant is going to take 65,442.4 seconds. Ok. So the difference 65, 0.4 seconds minus 64,800 seconds, which is the 1st 18 hours is going to be equal To 642.4 seconds. OK. So they walk for 18 hours And 642.4 seconds. Right now, we Wanna convert that seconds into minutes. OK. We've done the hours part. We've gotten the maximum number of full hours. 18. Now we're gonna do the same for minutes. So we have 642.4 seconds. Well, 642.4 seconds divided by 60 seconds per minute. The unit of seconds divides out and we're left with 10.706 repeated minutes. So we're gonna do the same thing we did with the hours. Ok, we have 10 full minutes and then a partial minute. Ok, that partial minute, that 100.7 oh six we're gonna deal with with seconds. We're gonna take just our full minutes. We have 10 full minutes And we know that there are 60 seconds in every minute. So the unit of minute divides. Oh, OK. 10 minutes multiplied by 60 seconds per minute. And this gives us 600 seconds. HM. So we started with 65,442. seconds. We found that we walked for 18 full hours Which left 642.4 seconds. Now we figured out, OK, we walk 18 hours plus 10 full minutes. What are we left with? Now? We were left with 642.4 seconds. Our 10 minutes took 600 seconds. And so we're left 642. seconds -600 seconds, which is equal to 42.4 seconds. See. All right. So putting this all together, we had 18 full hours. We had 10, 4 minutes And what was left over after counting for the 18 hours and the 10 minutes was 42.4 seconds. And so the time required For our participant to finish this walk is 18 hours, 10 minutes and 42.4 seconds. OK. If we round to the nearest second, this corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

Key Concepts

Unit Conversion

Rate and Time Calculation

Comparison of Times

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