Question

I am confused. Can somebody explain this to me?

Answer 1

Answer: If they worked together, it would take 31.5 minutes

Step-by-step explanation:

There's a certain formula for equations like this:

$\frac{1}{t1} +\frac{1}{t2}=\frac{1}{tb}$

t1= the time it took for the first person to complete the task.

t2= the time it took for the second person to complete the task.

tb= the time it took for both of them to complete the task.

We have the values for both t1 and t2, but not for tb.

t1= 45

t2= 105

tb= x

$\frac{1}{45} +\frac{1}{105} = \frac{1}{x}$

Now it's simple algebra, and all we need to do is solve for x

The LCM for both fractions is 315, so now we multiply BOTH sides of the equation by 315.

$\frac{315}{45} + \frac{315}{105} = \frac{315}{x}$

This will simplify nicely, so now we just need to get x on the other side.$7 + 3 = \frac{315}{x} \\\\\ 10*x = \frac{315}{x} * x$

$10x = 315 \\\\x = 31.5$