Question

A bee flies 10 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 8 feet per second. It is away from there for a total of 19 minutes. a What equation can you use to find the distance of the flowerbed from the hive?

Answer 1

Given that:

A bee flies 10 ft/s directly towards a flowerbed from its hive.

It stays at the flowerbed for 15 minutes and then flies directly back to the hive at 8 ft/s.

The total time it is away from there is 19 minutes.

Consider that speed is the ratio of distance traveled to the time taken. That is:

$s=\frac{d}{t}$

Let x represent the distance from the bee hive to the flowerbed, and d be the distance.

When speed was 10 ft/s, let the time be y

$\begin{gathered} 10=\frac{d}{y_{}} \\ \\ d=10y \end{gathered}$

When the speed was 8 ft/s, let time be z

$\begin{gathered} 8=\frac{d}{z} \\ \\ d=8z \end{gathered}$

Distance is unchanged, so

$10y=8z\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1)$

Since the total time is 19 minutes = 1140 seconds

We have the equation for time as:

$y+z=1140\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2)$

Solving (1) and (2) simultaneously, we can obtain the values for x and y, and these will help know the value for the required distance.