How to Solve this Algebra 1 word problem:

"A bee flies at 20 feet per second directly to a flowerbed from its hive.  The bee stays at the . . ."

Welcome to Can Do Math!  If you're in 8th or 9th grade and you need help with the following Algebra 1 word problem, you're in the right place.


A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 12 ​minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 17 minutes. 

  • What equation can you use to find the distance of the flowerbed from the​ hive?

  • How far is the flowerbed from the​ hive?

  

  1. The first step to solving this and any word problem is to read it out loud.  Don't worry about pronouncing the words correctly.  Rather, read the problem slowly to yourself, so that YOU can understand it.  You may need to read it several times in order to wrap your brain around it.
  2. The second step is to draw a picture.  Label the bee, the hive, and the flowerbed.  This will help you to visualize the problem.
  3. The third step is to return to what the word problem is asking us to find.  In this case, we get to find the distance from the flowerbed to the hive.

Can you think of a formula for distance?  One way to determine distance is to multiply rate by time.  In other words,


distance = rate X time

D = RT


This formula will help us to solve the problem.




One thing we need to make sure of is that we use consistent units of measurement.  This is a tricky word problem because it gives us some measurements in seconds and other measurements in minutes.  Let's convert the seconds to minutes: 


20 feet                 ?   feet

___________   =     _____________

1 second            60 seconds


In order to find how many feet the bee flies in 60 seconds, we multiply 20 by 60.  That gives us 1200.  In other words,


20 feet per second = 1200 feet per minute


We'll plug this into our equation later.


Now let's do the same with 16 feet per second:


16 feet                 ?   feet

___________   =     _____________

1 second            60 seconds


In order to find how many feet the bee flies in 60 seconds, we multiply 16 by 60.  That gives us 960.  In other words,


16 feet per second = 960 feet per minute


We'll plug this into our equation later as well.




Solving a word problem involves a lot of trial and error.  It also involves a lot of playing around with the information we're given.


Recall that the problem says, "The bee stays at the flowerbed for 12 ​minutes." 


It also tells us, "It is away from the hive for a total of 17 minutes."


So we can write the following equation:


[# of minutes it took to fly to flowerbed] + 12 minutes + [# of minutes it took to fly back to the hive] = 17 minutes


In other words,

[flight] + 12 + [return flight] = 17


Now, let's revisit this perenially useful formula:


distance = rate X time

D = RT


Another way of writing it is:

T = D/R

In other words,

time = distance divided by rate


This formula will be super-helpful in solving our equation above:


[# of minutes to flowerbed] + 12 minutes + [# of minutes back to hive] = 17 minutes


The number of minutes to and from the flowerbed is an expression of time (T).  So we can plug D/R in for each:


(D/R) + 12 + (D/R) = 17


The speed is the rate. 


Now, we don't know the distance, but we do know the rate. 


Let's plug in the rate, which we identified above. 

Since the bee's return flight was at a different speed, we have two different rates: 1200 feet/minute and 960 feet/minute.


(D/R) + 12 + (D/R) = 17

(D/1200) + 12 + (D/960) = 17

This is the equation we can use to find the distance from the flowerbed to the​ hive.




So our variable is D (for distance). We can choose any letter we like (such as x), but on this page I'm going to choose D for distance.


Since it's a given that the distance to the flowerbed is the same as the distance back from the flowerbed, we only have one variable. 


When we solve for D, we will have the answer to the second question.


Please write this equation down on paper and solve it by hand, by yourself.  It will make a lot more sense than if you only read the steps on this webpage.


(D/1200) + 12 + (D/960) = 17


  • First, let's get rid of the 12.

Subtracting 12 from both sides of the equation, we get:

(D/1200) + (D/960) = 5

  • Second, let's multiply the whole equation by 1200 X 960.  That will enable us to isolate the distance (D).


(D(1200)(960))/1200 + (D(1200)(960))/960 = 5(1200)960

960D + 1200D = 5(1200)960

2,160D = 5,760,000

  • Now, let's divide the entire equation by 2160 in order to solve for D (distance):

D = 5,760,000/2,160

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Thank you for visiting Can Do Math!  I hope you've found this page helpful in solving the following Algebra 1 problem:


A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 12 ​minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 17 minutes. 

  •     What equation can you use to find the distance of the flowerbed from the​ hive?

  •     How far is the flowerbed from the​ hive?