Tony is 1/2 of a mile ahead of Laura on a jogging path. If Tony is running at 5 miles per hour, and Laura is running at 7 miles per hour, how long will it take Laura to catch up with Tony?

Another way of looking at this problem, is that Laura will "gain" 2 miles on Tony in 1 hour. Why? She is going 7 miles in 1 hour, while Tony is only going 5. 7-5 = 2.

However, Tony is only .5 miles ahead and the question asks how long will it take for her to catch up, not to overtake him or beat him in some race.

I would make a simple ratio here. If in 1 hour/she beats him by 2 miles, x hours/she beats him by .5 miles.  

Another way to write that is 1/2 = x/.5

If you solve the equation, you get (by cross-multiplication) 2x = .5, x = .5/2, x =1/4.

Now, we are dealing with hours, so since there are 60 minutes in one hour, multiple the value you obtain for x by 60 minutes (60*1/4) = 15 minutes.  

Therefore, it will take Laura 1/4 of an hour, or 15 minutes, in order to catch up with Tony

Step-by-step explanation:

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>