Questions on Word Problems: Travel and Distance answered by real tutors!

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Question 161322: At noon a private plane left austin for los angeles, 2100km away, flying at 500km/h. one hour later a jet left los angeles for austin at 700k/m. At what time did they pass each other?
Click here to see answer by scott8148(6628)

Question 161347: two cyclists start from the same point and ride in opposite deirections. ONe cyclist rides twice as fast as the the other. In 3 hours they are 81 miles apart. Find the rate of each cyclist.
Click here to see answer by checkley77(12569)

Question 161391: An airplane travels 600 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.
Click here to see answer by checkley77(12569)

Question 161430: Vincent's boat will go 13 miles per hour in still water. If he can go 14 miles downstream in the same amount of time as it takes to go 8 miles upstream, then what is the speed of the current?
Click here to see answer by nerdybill(6948)

Question 161431: A river has a current of 4mph. Find the speed of Simon's boat in still water if it goes 40 miles downstream in the same time as 24 miles upstream.
Click here to see answer by checkley77(12569)

Question 161390: The speed of a stream is 4mph. If a boat travels 80 miles downstream in the same time that it takes to travel 40 miles upstream, what is the speed of the boat in still water?
Click here to see answer by checkley77(12569)

Question 161486: 2. The equation D=1.2 square root of h. gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
b. Long’s Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain your answer.

Click here to see answer by checkley77(12569)

Question 161485: Hint for this assignment: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: w=Cr^-2 , where C is a constant, and r is the distance that the object is from the center of the earth.
a. Solve the equation for r.
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
c. Use the value of C you found in the previous question to determine how much the object would weigh in
i. Death Valley (282 feet below sea level)
ii. The top of Mt McKinley (20,320 feet above sea level)

Click here to see answer by ankor@dixie-net.com(15622)

Question 161495: If Jamar can run 3/5 of a mile in 2 minutes 30 seconds, what is his rate in miles per minute?
Please show all work. I appreciate it! Thanks!

Click here to see answer by scott8148(6628)

Question 161247: The product of a 2-digit number and 101 contains the digits of the 2-digit number repeated twice. For example 42 X 101 = 4242. What should you multiply a three-digit number by in order to have the product repeat the digits ?
Click here to see answer by scott8148(6628)

Question 161411: Can you please help with this word problem? Thanks

The period T (time in seconds for one complete
cycle) of a simple pendulum is related to the length L
(in feet) of the pendulum by the formula 8T^2= pi^2L. If a
child is on a swing with a 10-foot chain, then how long
does it take to complete one cycle of the swing?
Click here to see answer by Alan3354(30924)

Question 161569: In 1/4 of an hour more time ,Jack , riding a bicycle at 12 mph, rode 6 mies farther than Tom, who was riding his bycycle at 10 mph. How long did Jack ride?
Click here to see answer by Alan3354(30924)

Question 161577: Allie invested a certain amount of money at 5% interest, and $1500 more than that amount at 6%. Her total yearly interst income was %420. How much did she invest at each rate?
Click here to see answer by oscargut(891)

Question 161571: How many liters of pure alcohol must be added to 10 liters of a 30% solution to obtain a 50 % solution?
Click here to see answer by KnightOwlTutor(293)

Question 161585: A river is flowing at a rate of 5 km/h. A boat travels 12km upstream and 36km downstream in a total of 9hours. What is the speed of the boat in still water?
Click here to see answer by KnightOwlTutor(293)

Question 161573: A total of $4000 was invested, part of it at 8% and the remainder at 9%. If the total interest income amounted to $350, how much was invested at each rate?
Click here to see answer by jojo14344(1512)

Question 161570: If 500 is invested at 6% interest, how much additional money must be invested at 9% so that the total return for both investments averages 8% ?
Click here to see answer by checkley77(12569)

Question 161603: Distance is 1200
The Wallaces take a trip by train and plane
The train is going 48 mph and takes 2 hrs longer than the plane
The plane is going 240 mph.
What is the total time of the trip?
I know this is a d=rt problem and I know that the train takes two hours longer. I'm just not sure how to set up the equation and is there two equations since I am solving for the entire time of the trip?
Thank you, Rose
Click here to see answer by nerdybill(6948)

Question 161642: Benny is traveling at a speed of 30 mi/h. What is his speed in feet per second?
Click here to see answer by checkley77(12569)

Question 161625: At noon Tom leaves in his boat from a dock and heads south. He travels at a rate of 25 mph. Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. If she travels at a rate of 30 miles per hour at what time will she catch up with Tom?
Click here to see answer by checkley77(12569)

Question 161627: hi to all of you who help. can you please help me? A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. if the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-fourth greater, the person would have traveled only 1315 miles in the same length of time.find the speeds of the plane and ship.thanks for the help.
Click here to see answer by gonzo(654)

Question 161670: A motorboat left a harbor and traveled to an island at an average rate of 15 knots. The average speed on the return trip was 10 knots. If the total trip took 7.5 hours, how far is the harbor from the island?
Click here to see answer by checkley77(12569)

Question 161833: I need some help please.
Juniors boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time it takes to go 9 miles upstream, then what is the speed of the current?
Click here to see answer by checkley77(12569)

Question 161894: Two cars, which are 550 miles apart and whose speeds differ by 2 miles per hour, are moving toward each other. If they meet in 5 hours, find the speed of each car.
Click here to see answer by checkley77(12569)

Question 161899: Two cars, which are 550 miles apart and whose speeds differ by 2 miles per hour, are moving toward each other. If they meet in 5 hours, find the speed of each car.
Click here to see answer by checkley77(12569)

Question 161852: Two trains leave the same station and travel in opposite directions. One is traveling east at 56 mph, and the other is traveling west at 70 mph. In how many hours will they be 1080 miles apart?
a. 6 hours
b. 10 hours
c. 8 hours
d. 12 hours
Click here to see answer by edjones(7569)

Question 161991: Please help, thank you.
At 1:00 p.m., a car leaves a city and travels north at a rate of 55 mi/h. An hour later, a second car leaves the city and travels south at a rate of 60 mi/hr. At what time will the two cars be 285 miles apart?
Click here to see answer by nerdybill(6948)

Question 161980: Please help with this problem. I have tried to look at other similar problems to help guide me, but is not working.
--> A stamp collection consists of 3, 8, and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is $2.47. Find the number of 8 cent stamps in the collection. [Fifteen points for the correct algebra equation and five points for solving the equation.
Click here to see answer by vleith(2825)

Question 161981: Please help.
A cyclist traveled at a rate of 32 mph to visit a nearby town. The cyclist averaged 10 mph on the return trip. If the round trip took 6.3 hours, find the distance to the nearby town. [Fifteen points for the correct algebra equation and five points for solving the equation.
Click here to see answer by scott8148(6628)

Question 162021: Joel drives his car for 20km at a certain speed.At a distance,he increases his speed by 5 km per hour and drives for an additional 20km.If the total trip taken is 1 hour,what is his original speed?
Click here to see answer by ankor@dixie-net.com(15622)

Question 162015: The Metro Rail travels 240 km at a uniform rate.If the speed had been 8 km per hour more,the journey would have taken 1 hour less.what is the speed of the train?
Click here to see answer by josmiceli(9645)

Question 162056: Please help!
A plane carries enough fuel for 10 hours of flight at an airspeed of 150 miles per hour. How far can it fly into a 30 mph headwind and still have enough fuel to return to its starting point? (This distance is called the point of no return.)

Click here to see answer by ankor@dixie-net.com(15622)

Question 162169: Raleigh, NC is about 120 miles inland from the nearest point on the Atlantic coast; Savannah, Ga is about 300 miles south of that point down the coast. Assuming the coast is a straight line going north-south, C is the point along the coast directly east of Raleigh. It costs 2 cents per mile to transport a ton of shrimp by truck and 1 cent per mile to transport them by ship. The Savannah Shrimp company wants to find the point, P, on the Atlantic Coast to which it should truck its shrimp before loading then aboard to cargo ship in order to minimize the total cost of transporting them from Savannah to Raleigh.
a. Set up the function which the Savannah Shrimp Company must minimize.
b. Find the position of P which minimizes cost.
Click here to see answer by ankor@dixie-net.com(15622)

Question 162216: Sam hiked up a mountain at a rate of 2.5 mph and returned along the same path at a rate of 3 mph. His total hiking time was 11hr. How long was the hiking trail?
Click here to see answer by checkley77(12569)

Question 162275: 2 automobiles start together and travel in the samer direction. the first can travel 2 times as fast as the slower one. at the end of 2 hrs. they are 60 kms. apart. how fast does each of them travelling?
Click here to see answer by checkley77(12569)

Question 162271: a helicopter travels 630 kms. at the same time that a car travels 210 kms. If the helicopter travels 60 km. per hour faster than the car, how fast does each of them travel?
Click here to see answer by josmiceli(9645)

Question 162289: A train leaves a station and travels north at 80 km per hour. three hours later a second train leaves on parallel tack and travel in the same direction at 120 km per hour. how far from the station will they meet?
Click here to see answer by jojo14344(1512)

Question 162311: Alexander and Judy are 32 miles apart on a calm lake paddling toward each other. Alexander paddles at 4 miles per hour, while judy paddles at 7 miles per hour. How long will it take them to meet?
Click here to see answer by ankor@dixie-net.com(15622)

Question 162019: ROSE DROVE HER CAR FROM HER HOME TO THE PROVINCE AND BACK,A TOTAL DISTANCE OF 120KM.HER AVERAGE SPEED RETURNING WAS 3KPH SLOWER THAN HER AVERAGE SPEED GOING TO THE PROVINCE.IF HER TOTAL DRIVING TIME WAS 9 HOURS ,WHAT WAS HER AVERAGE SPEED IN GOING TO THE PROVINCE?
Click here to see answer by ankor@dixie-net.com(15622)

Question 162351: Mr. Turner has a motorboat that can travel 14 mph in still water. He wishes to take a trip on a river whose current flows at the rate of 2 mph. If he has 7 hours at his disposal, how many hours should he spend on the first part of his trip going downstream before returning upstream to his starting point?
Click here to see answer by ankor@dixie-net.com(15622)

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