A bus travels at a constant speed from point A to point B, which are 600 km apart. Some time later, a motorcyclist begins the trip from A to B, traveling at 100 km/h. The motorcyclist overtakes the bus at 150 km from A, and continues on to point B. The motorcyclist arrives at B, rests for 1 hour, and begins the return trip to A, crossing paths with the bus. When the bus arrives at B, the motorcyclist is 200 km from B. How far from B did the motorcycle and bus meet the second time?

Step-by-step explanation:

the motorcyclist starts x hours after the bus.

it takes the motorcyclist 1.5 hours to meet the bus the first time, 6 hours to reach B, rest 1 hour and go another 2 hours before the bus arrives at B.

so, the bus needs

x + 9 hours to reach B.

x + 1.5 hours for 150 km (for the first meeting with the motorcyclist).

the speed of the bus is 600/(x + 9) km/h or 150/(x + 1.5) km/h.

so,

600/(x + 9) = 150/(x + 1.5)

4/(x + 9) = 1/(x + 1.5)

4(x + 1.5)/(x + 9) = 1

4(x + 1.5) = x + 9

4x + 6 = x + 9

3x + 6 = 9

3x = 3

x = 1

the motorcyclist starts 1 hour after the bus.

the speed of the bus is

600/(x + 9) = 600/(1 + 9) = 600/10 = 60 km/h

when the motorcyclist is starting its return trip, he is 7 hours after his start, and the bus is 7+x = 7+1 = 8 hours after its start, that means at

8×60 = 480 km of its total trip of 600 km.

120 km are still left for the bus to go.

from that point on both travel the same time y going with their speeds until they meet the second time.

the motorcyclist travels 100y km building up distance from B, while the bus travels 60y km reducing the 120 km distance from B.

when they meet the second time, the distance from B for the motorcyclist is the same as the remaining distance for the bus.

so,

100y = 120 - 60y

160y = 120

y = 120/160 = 3/4 = 0.75 hours

so, they meet at

100 × 0.75 = 75 km from B.

I need help Please UwU Thanks!

please help quick!! A fully loaded and fueled spacecraft can weigh close to million pounds. What is this weight converted to​ tons?

To graph the point (4, -7) on the coordinate plane, start at the origin. Move 4 units _______ and 7 units ________ .
choices:
a
right.....down
b
left....down

Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that all have three cookie flavors and the same number of each flavor per bag.

How many cookies of each type are in each bag if he can make 16 bags without having any cookies left over?

A clothing store uses a markup of 60% on all items they purchase to sell. What is the retail price of a pair of shoes that originally costs $350?

How old is Eduardo if he will be 82 years old in six years? Write an equation. Use lower case x as your variable and no spaces. Just as we did in class, make sure that the variable is in the problem, not in the solution

How do you identify the constant of proportionality when given a graph?

Describe the error in finding the median of the data.

I would like some help please :). I'll give brainiest to right answer.

Help I need to know?

Please help me i will mark brainliest and thank you. ASAP!!!

Please help and explain how you got your answer please!

A certain fraction is close to 30%. What might it be?

Need with question b

In Britain a Value Added Tax (VAT) of 17% is added to most purchases. If a skit costs $58.50 including tax, what is the price of the skirt before tax?

HELP FAST.


Which of the following values of t will result in a true statement when substituted into the given equation? A. t = 8 B. t = -8 C. t = 11 D. t = -12.

7. Draw a circle around the expression which is greatest when n is a negative number?
n²

A. n-2
B. 2n
C. n/2
D. 2/n​

The Cerca Middle School Student Committee is sponsoring a Math Fair for parents and students. Mr. Tilton's homeroom class is designing some of the questions for the students.

Nina created this pattern using trapezoid tiles.

How many unit trapezoids will be in pattern 16?

A hamburger and fries costs $15, water cost $4, and an ice cream costs $5. Do I have enough money to buy all three items with the money I have left over after buying my ticket? Explain why or why not.

Find the area of this circle. Use your calculators value of pi. Round answers to the nearest tenths place.

help with my worksheet please

Write the formula for the parabola that has x- intercepts (1.3,0) and (-1.3,0), and y- intercept (0,169).

Question 9)
Help me please

Which statement best describes the relationship shown in the table?
Input 0 1 2 3 4
Output 1 3 9 27 81
As input increases by 1, output doubles.
As input increases, output increases to 81 then begins to decrease.
As input increases by 1, the output triples.
As input increases, output decreases.

There is a closed carton of eggs in Mai's refrigerator. The carton contains eggs and it can hold 12 eggs.
What does the inequality e<12 mean in this context?

7th grade math <3 pls help heh

On average 70% of customers order vanilla yogurt, and 30% order chocolate yogurt. In the following random number table, numbers 00 through 69 represents vanilla yogurt and numbers 70 through 99 represents chocolate yogurt.

Turn these equations into Standard Form. Pls show the steps on how you did it.
y=-2x-3/2
y=4/5x-10
y=11/8x+6
y=1/3x-2
y=-6/5x-3

A hardware store sells flower containers that are shaped like rectangular prisms. The dimensions of the container are shown below. Max needs to fill the container with dirt. What is the volume of the rectangular prism in square feet?

I need help 8th grade math