Question

Hank has picked 1.3 pounds of berries and picks about 0.75 pounds per min. Tom has picked 2.5 pounds of berries and picks about 0.5 pounds per minute. In how many minutes where are picked at least as many pounds of berries as Tom?

Answer 1

Hank: 1.3 pounds at a rate of 0.75 pounds per minute

Tom: 2.5 pounds at a rate of 0.5 pounds per minute

rate is given by

r = p / t

where p is the number of pounds picked during a fixed time

The number of berries picked by Hank during a certain time is given by the following equation

$H=1.3+0.75t$

For Tom, the equation is the following:

$T=2.5+0.5\cdot t$

Now, we need to find a time t when T and H are the same

$\begin{gathered} H=T \\ 1.3+0.75t=2.5+0.5t \end{gathered}$

We now just need to solve for t

Let's find t step by step

$\begin{gathered} 1.3\cdot\: 100+0.75t\cdot\: 100=2.5\cdot\: 100+0.5t\cdot\: 100 \\ 130+75t=250+50t \\ 130+75t-130=250+50t-130 \\ 75t=50t+120 \\ 75t-50t=50t+120-50t \\ 25t=120 \\ \frac{25t}{25}=\frac{120}{25} \\ t=\frac{24}{5} \end{gathered}$

Which is the same as t=4.8