if the length of the entire route is 7 miles, PH= 5.2 miles,and PN ~= HM, what is the value of NH in miles?

Question

gosh i cant get anything its like a brand new language this is what i see @%$^!@*& 

 

PLEASE HELP

 

a bus follows a straight route down a road.the route starts at the post office at point P, proceeds to a neighborhood at point N,goes on to the hotel at point H and ends at the mall at point M.

Answer 1

I think that the best way to see this problem is with a picture. We know that the bus travels in a straight line and that it makes 4 stops at P,N,H,and M. This means that these four points must lay on the line at some distance apart.

 

(i cannot upload a picture so i will do my best to use symbols to make a sketch)

 

P → N → H → M

 

The problem tells us that the length of the entire route from P to M is 7 Miles. The segment from P to H is 5.2 miles and that segment PN is the same length as segment HM. 

 

Now let's write some equations. 

We know that 

 

Line PM =Segment PN +Segment NH + Segment HM,  using the numbers we stated above we have

 

7=5.2+HM

 

Which means segment HM=1.8 miles, we need this to solve for segment NH.

 

Now recall that segment PN and segment HM are the same length, so since HM is 1.8 miles then segment PN=1.8 miles.

Also recall that Segment PH, which is made up of PN and NH is 5.2 mile.

 

So 5.2=PN +NH, we know that PN=1.8

 

So 5.2=1.8 +NH

 

So 3.4 miles =NH

 

We can check our work because all 3 segment should add up to 7 miles.

3.4+1.8+1.8 =7.

 

Good Luck!