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Word Problems: Travel and Distance

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Question 16947: A student leaves the university at noon, bicycling south at a constant rate. At 12:30pm a second student leaves the same point and heads west, bicycling 7mph faster than the first student. At 2:00pm, they are 30 miles apart. How fast is each one going? Also, how would I properly set-up this equation?
Below is what I thought is the answer, please let me know where I went wrong?
r=d/t
30/2 = 15mph (first student)
30/1.5 = 20 + 7 = 27 mph (second student)
Click here to see answer by venugopalramana(3286)

Question 17610: A plane travels with a tail wind (100) miles to the nearest town in (60) minutes. The plane then travels back (100) miles with a head wind. The travel time is (40) min more than the first trip. What is the speed of the wind, and the speed of the plane?
Click here to see answer by xcentaur(357)

Question 17655: Hi there,
I don't get this problem with rational expressions! Could someone please help me work out this problem before class?
v=4/3(pi symbol here) r^2h for h
Thank you
AC
Click here to see answer by rapaljer(3610)

Question 17656: Hi there,
I don't get this problem with quadratic formulas! Could someone please help me work out this problem before class?
-x^2 -5x + 1 = 0
Thank you
AC
Click here to see answer by shirsenduban(10)

Question 17659: Hi there,
I don't get this problem with finding the perfect square trinomial whose first terms are given. I really hate fractions on this one. Could someone please help me work out this problem before class?
x^2 + 2/3x
Thnx very much
Click here to see answer by xcentaur(357)

Question 17657: Hi there,
I don't get this problem with quadratic formulas! Could someone please help me work out this problem before class?
2t^3 -6t + 1 = 0
Thank you
AC
Click here to see answer by xcentaur(357)

Question 17826: Greetings!
Okay, who can help me understand word problems? I really need to know how to break down this problem and solve it. Could someone please help understand!
Problem: If 220 out of 500 voters surveyed said that they would vote for the incumbent, then how many voters could the incumbent expect out of the 400,000 voters in the state?
Thanks to all.
Click here to see answer by venugopalramana(3286)

Question 17825: Greetings!
Okay, who can help me understand word problems? I really need to know how to break down this problem and solve it. Could someone please help understand!
Problem: Alonzo travels 230 miles in 3 hours, how many miles miles traveled in 7 hours?
Thanks to all.
Click here to see answer by venugopalramana(3286)

Question 17807: Please help!!!
Preston antifreeze is 20% antifreeze and Icefree is 12% antifreeze. How much of each should be used to get a 22 quart mixture of 15% antifreeze?
Thanks in advance

Click here to see answer by venugopalramana(3286)

Question 17806: Please help!!!
Susan's communte to work in the morning takes 45 minutes and coming home she is able to drive 10 miles per hour faster, so it only takes 30 minutes, how far is her communte (one-way)?
thanks in advance
Click here to see answer by venugopalramana(3286)

Question 17945: If Mr. X leaves now and drives 66 km/hr, he will reach Tuscaloosa in time for an appointment. On the other hand, if he has lunch first and leaves in 40 minutes, he will have to drive 90 km/hr to make the appointment. How far away is Tuscaloosa? (thanks for the assistance).
Click here to see answer by venugopalramana(3286)

Question 17944: Mr. X biked 2.5 hrs up a mountain. Rested for 30 minutes. Biked down in 1.5 hrs. How far did he bike, if his rate of ascent was 3 km/hr less than his rate of decent?
Click here to see answer by venugopalramana(3286)

Question 18083: A cheetah is 300 feet from its prey. It starts to sprint toward its prey at 90 feet per second. At the same time, the prey starts to sprint at 70 feet per second. When will the cheetah catch its prey?
Click here to see answer by tennis_math(7)

Question 18396: Suppose that a ball is dropped from a height of 30ft and that each bounce reaches to 3/8 of the previous height. How high will the ball bounce on the second bounce?
Click here to see answer by MelanieBCC(40)

Question 18444: Joe traveled against the wind in a small plane for 3 hr. The return trip with the wind took 2.8 hr. Find the speed of the wind if the speed of the plane in still air is 180mph.
Click here to see answer by venugopalramana(3286)

Question 18553: If a car travels at a constant rate of 66 miles per hour, how many miles does it travel in 20 minutes?
Click here to see answer by piglet162431(90)

Question 18597: Driver A drove 150 miles in the same amount of time that it took an airplane to travel 600 miles. The speed of the plane was 150 mph faster than the speed of the car. What is the speed of the plane. I realize the plane is 4x faster than the car but I am struggling to write the equation. please help
Click here to see answer by mmm4444bot(95)

Question 18535: A boat traveled 25km upstream. On the return trip downstream, the boat traveled 5km per hour faster. It the trip took 10 minutes less time, what was the speed of the boat as it traveled upstream?
The answer is 25 km/hr but I don't know how to get to it!
Thanks for any help you can give!
Click here to see answer by xcentaur(357)

Question 18586: HELP !!
A passenger train's speed is 60 mi/h and a freight train's speed is 40mi/h.The passenger train travels the same distance in 1.5 h less time than the freight train.How long does each train take to make the trip?
Thanks for your help !!
Click here to see answer by wuwei96815(245)

Question 18707: Please help me out with this one. I went thru the other questions and didn't see this type of question. Thanks
Joe traveled 290 miles east of St. Louis. For most of the trip he averaged 70mph, but for one period of time he was slowed to 20mph due to a major accident. If the total time of travel was 7 hours, how many miles did he drive at the reduced speed?
Click here to see answer by venugopalramana(3286)

Question 18817: A troop of scouts hiked to the city at a rate of 2 mph. they rode back at a rate of 18 mph. If the round trip took 10 hours, how far is the city? What is the formula to solve this problem?
Click here to see answer by yuvaraja(2)

Question 18170: I could really use some help on this, I am terrible at wordproblems.
Tom Quig traveled 240 miles east of St. Louis. For most of the trip he averaed 60mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 6 hours, how many miles did he drive at the reduced speed?
Here is what I did :
(60)**(60)
240 =3x
80 =x

Am I even close on this answer.
Please help, thank you so much.
lizzy

Click here to see answer by venugopalramana(3286)

Question 18913: A car started out from Memphis toward Little Rock at the rate of 60 km/h. A second car left from the same point 2h later and drove along the same route at 75km/h. How long did it take the second car to overtake the first car?
Click here to see answer by Paul(988)

Question 19022: A plane flies 720 mi against a steady 30-mph headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane's speed in still air?
Click here to see answer by MelanieBCC(40)

Question 19037: If two planes leave the same airport at 1pm, how many miles apart will they be at 3pm if one travels north at 150 mph and the other travels directly west at 200 mph?
Click here to see answer by MelanieBCC(40)

Question 19107: It takes a plane 40 min. longer to fly from boston to los angeles at 525 mi/h than it does to return at 600 mi/h. how far apart are the cities?
Click here to see answer by Paul(988)

Question 19122: ollie Carr has just enough money to rent a canoe for 1 1/2 hours. how far out on a lake can he paddle and return on time if he paddles out at 2 km/h and back 4 km/h?

Click here to see answer by mmm4444bot(95)

Question 19130: Hi, I'm stuck on the following problem: On a sales trip, Gail drive 600 miles to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 miles per hour slower. Total time for the round trip is 22 hours. Find Gail's average speed on each part of the trip.
Any help would be appreciated. Thank you so much!!
Click here to see answer by mmm4444bot(95)

Question 19151: OK...Brent rides a moped at 24 miles per hour. His wife Jan rides in the opposite direction at 8 miles per hour. How much time will pass when they are 24 miles apart? I know the answer is 3/4 hour, but I'm having a hard time getting that using the old rate x time = distance method. Can you bail me out?
Click here to see answer by venugopalramana(3286)

Question 19150: Joe digs a ditch in 3.2 hours.
Joe working with George can did the same length ditch in 2.7 hours.
How long would it take George to dig the ditch by himself.

Click here to see answer by venugopalramana(3286)

Question 19230: The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet? I figured 1296 = x(6)square but not able to complete.
Click here to see answer by Earlsdon(4898)

Question 19282: If it takes 18 minutes to travel by bicycle from point A to B in a headwind and
6 minutes to travel from B to A with a tailwind, how long will it take to cover this distance with no wind?
SEE THIS WHICH IS SIMILAR TO YOUR PROBLEM AND SOLVE YOUR PROBLEM
A boat travels at the speed of 20 Miles per hour in still water. It travels 48 miles up stream, and then returns to the starting point in a total of five hours. The speed of the current is ____ miles per hour.
distance =speed * time..or...time=distance/speed
Still water speed of boat =20 mph
let the stream velocity be =x mph
so its speed upstream =20-x
its speed down stream =20+x
distance travelled either way =48 miles
time taken to travel upstream=48/(20-x)
time taken to travel down stream =48/(20+x)
total time of travel =5 hours..hence
[48/(20-x)]+[48/(20+x)]=5
48[(20+x+20-x)/((20-x)(20+x))]=5
48*40=5(20^2-x^2)=2000-5x^2
5x^2=2000-1920=8=
x^2=80/5=16
x=4 mph
Click here to see answer by venugopalramana(3286)

Question 19478: Please help me with this problem I have exhausted all of my resources to try and figure it out.
On a windy day Yoshiaki found that he could go 16mi downstream and then 4mi back upstream at top speed in a total of 48min. What was the top speed of Yoshiaki's boat if the current was 15mph?

The answer in the back of the book is 25mph, but I can't seem to figure out how they came up with that answer. We are working with quadratic equations. Here is what I have tried:
______________D_____R________T_______
upstream:_____4mi___x-15___4/(x-15)
downstream:___16mi__x+15___16/(x+15)
_____________________________________
4/(x-15) + 16/(x+15) = 48
I cannot seem to come up with the answer 25, I must be doing something wrong in the form of the equation. Please Help!!
Click here to see answer by xcentaur(357)

Question 19596: A freight train and an express train leave towns 390 km apart, traveling toward one another. The freight train travels 30 km per hour slower than the express train. They pass one another 3 hour later. What are their speeds?
Thanks for your help.
Click here to see answer by venugopalramana(3286)

Question 19770: I'm very bad at word problems and this one seems to make me more confused!!
Train A leaves depot A and travels to depot C 400 miles away and Train B leaves depot B one hr later and travels 150 miles to depot C. If Train A is travelling 10mph faster than train B and they arrive at depot C at the same time, how fast was each train travelling?
Thank you sooo much!!!!
I got this far but that's not really an equation: A=400miles(10+b) B=150miles(A-60min)
Click here to see answer by Paul(988)

Question 19788: An afternoon sightseeing cruise up river and back down river is schedualed to last 1 hour. The speed of the current is 4kh/h, and the speed of the riverboat in still water is 12km/h. How far upstream should the pilot travel before turning around?
Click here to see answer by xcentaur(357)

Question 19831: This is very urgent.. It's due soon and I can't figure it out!
Charles Lindbergh estimated that at the beginning of his flight his speed was at 95mph. After travelling 4000 miles, his speed dropped to 75mph. Find the formula for the linear equation representing his speed and distance.
Thank you
Click here to see answer by Paul(988)

Question 19855: A 10 cm cube of material has a mass of 2.2 kg. What is its density?

Click here to see answer by christinaaa192(28)

Question 20133: solve.
Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling? Explain your steps as you solve.
thanks
Click here to see answer by Paul(988)

Question 20198: A race track measures 8 miles long. If an automobile completes the track in exactly 3 minutes, what is its average rate of speed in miles per hour?
Click here to see answer by wuwei96815(245)

Question 20151: JAY DROVE 284 KM AT AN AVERAGE RATE OF 71 KM/HR. HOW LONG DID THE TRIP TAKE?
Click here to see answer by suresh(20)

Question 20463: Lynn walked for 2 hours then ran for 30 minutes, if she ran twice as fast as she walked and she covered 12 miles altogether how fast did she walk?
Click here to see answer by Paul(988)

Question 20507: Science and medicine. Martina leaces home at 9 A.M., bicycling at a rate of 24mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?
Click here to see answer by wuwei96815(245)

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