Mathematics, 16.09.2019 21:20 LindaCat78

Two motorcycles leave home at the same time, heading directly toward each other. they are a total of 196 miles apart. the first motorcycle travels at 65 miles per hour. the second motorcycle travels at 75 miles per hour. how long will it take for the two motorcycles to meet?
1.4 hours
2.4 hours
19.6 hours
5.2 hours

Answers: 3

Show answers

Answers

Answer from: Frankie103947

It is going to take 1.4 hours for the two motorcycles to meet.

Step-by-step explanation:

Understanding the problem:

The position of both motorcycles can be modeled by the following first order equation:

S(t) = S(0) + vt

In which S(t) is the position at the instant t, S(0) is the initial position, v is the speed in miles per hour and t is the time in hours.

To solve this problem, we have to model the equation $S_{1}(t)$ for the position of the first motorcycle and $S_{2}(t)$ for the position of the second motorcycle. They are going to meet at the instant t in which

$S_{1}(t) = S_{2}(t)$

I will also suppose that the positive direction is the direction from motorcycle 1 to motorcycle 2. One motorcycle moves in the positive direction, other in the negative, since they are heading directly toward each other. For the starting positions, one is at the position 0 and the other at the position 196. This is because they are a total of 196 miles apart.

The position of motorcycle 1:

I am going to say that motorcycle 1 is at the position 0. So S(0) = 0 . The first motorcycle travels at 65 miles per hour. I am going to say that motorcycle 1 travels in the positive direction, so v = 65 . So, the equation for the position of motorcycle 1 is:

$S_{1}(t) = 65t$

The position of motorcycle 2:

Since the motorcycle 1 starts at the position 0, the second motorcycle has to start at the position 196, so S(0) = 196 . Since the motorcycle one travels in the positive direction, the second is traveling in the negative direction, at 75 miles per hour, so v = -75 . So, the equation for the position of motorcycle 2 is:

$S_{2}(t) =196 - 75t$

How long will it take for the two motorcycles to meet?

$S_{1}(t) = S_{2}(t)$

65t = 196 - 75t

140t = 196

$t = \frac{196}{140}$

t = 1.4 hours

It is going to take 1.4 hours for the two motorcycles to meet.

Answer from: Quest

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.

Answer from: Quest

pretty sure its b

step-by-step explanation:

why? because i noticed a pattern. 60 120. those numbers without the zero, make the 6 times tables leaving your answer to be b since 6 times 4 is 24 and adding a zero making it 240.

Another question on Mathematics

Mathematics, 21.06.2019 21:00

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Answers: 3

Answer

Mathematics, 21.06.2019 23:30

What is the explicit rule for the sequence in simplified form? −1,−4,−7,−10,−13… an=4−5n an=−4−3n an=2−3n an=−6−5n

Answers: 1

Answer

Mathematics, 22.06.2019 03:00

Which is the factored form of the polynomial p(x) shown here?

Answers: 1

Answer

Mathematics, 22.06.2019 05:00

Sade bought 21 1/2 lb. of ground beef. he used 1/4 of the beef to make tacos and 2/3 of the remainder to make quarter-pound burgers. how many burgers did he make?

Answers: 3

Answer

You know the right answer?

Two motorcycles leave home at the same time, heading directly toward each other. they are a total of...

Questions