Answer:
420 miles
Step-by-step explanation:
We know that
in the triangle TQS
<span>applying the Pythagorean theorem
QS</span>²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1
in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2
in the triangle QTR
TQ²=TR²+36-----------> equation 3
<span>I substitute 1 and 2 in 3
</span>18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units
the answer is
TS=6√6 units
<span>6 is the square root of 6 units</span>
Answer:
I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.
Now let's make a table:
distance = rate * time
Train 1
Train 2
We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table
distance = rate * time
Train 1 r
Train 2 (r + 12)
Then it says "after 2 hours", so the time for both trains is 2 hours:
distance = rate * time
Train 1 r * 2
Train 2 (r + 12) * 2
Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:
2r + 2r + 24 = 232 and
4r = 208 so
r = 52
This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph
Step-by-step explanation:
Answer: C 4
Step-by-step explanation:
Use the formula: distance = rate x time
We can say that train 1 travels a distance of x, and train 2 travels a distance of 700 - x
The rate of train 1 is 75 mph, and the rate of train 2 is 100 mph
The time traveled for the two trains will be the same. We can represent that with the variable t.
We have the following equation for train 1:
x = 75t
For train 2, we have this equation:
700 - x = 100t
Use the Substitution Method by replacing x in the equation for train 2 with the value 75t.
700 - 75t = 100t
700 = 175t
700/175 = 4 hours.
It will take 4 hours for the two trains to meet.
Answer:
B
Step-by-step explanation:
