A bee flies at 9 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 15 minutes, and then
flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 19 minutes. a. What equation can you use to find the distance of the flowerbed from the hive? b. How far is the flowerbed from the hive?
Answer: A) What equation can you use to find the distance of the flowerbed from the hive? You can use the formula distance=time*speed
B) How far is the flowerbed from the hive? 14.4 feet
Explanation: 1) We can set up a system of equations since there are many values that we don’t know, like how long the bee took to get to the flowerbed and back:
Variables: a=the time it took for the bee to go to the flowerbed b=the time it took for the bee to come back to the hive
Equation 1: Distance when the bee went to the flowerbed=distance when the bee came back to the hive
Equation 2: a+b+15=19 (In total it took the bee 19 minutes, but it stayed at the flowerbed for 15 minutes. a and b are how long it took to get there and back)
2) Then, we input the values in the first equation:
9*60*a=6*60*
The formula we use on both sides of the equation is d=t*s since both sides refer to the distance.
The reason we multiplied 60 to the speeds is because the speeds were in seconds, whereas the time values in the question are all minutes (ex. 9ft/s, 15 minutes on the flowerbed, etc.)
3) Then, we evaluate the first equation:
9*60*a=6*60* Divide both sides by 60 9a=6b Divide both sides by 3 (we do this to simplify the numbers) 3a=2b
4) Now, we move around the second equation to bring into the first equation:
a+b+15=19 Combined like terms a+b=19-15 a+b=4 a=4-b
5) Bring the second equation into the first:
3a=2b 3(4-b)=2b Multiply the parentheses 12-3b=2b Combine like terms 12=2b+3b 12=5b Divide both sides by 5 (to cancel it out) 12/5=5b/5 12/5=b b=2.4 minutes
6) From here, we can solve for the distance.
Distance=time*speed Because we found b, the time it took for the bee to come back to the hive, we need to use the same speed Distance=2.4*6 Distance=14.4
I hope this helps! If it did, a brainliest would be much appreciated :)
An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement. To achieve our goal, we use two principles of equality, the addition principle and the multiplication principle.
