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

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So I had a kinda hard test today...well it was easy until this hard head wind/tail wind problem came up. The problem went like this Johnny went head wind (east to west I believe) from Miami to San Francisco 2100 miles at 5.6 lies per hour. When this other person (a girl) went tail wind (west to east) from San Francisco to Miami 2100 miles too but only took 4.8 miles per hour...what is the air speed and the wind speed?

The way you have it doesn't make sense.  All the planes I've seen fly a little
faster than 4.8 miles per hour, because you can walk that fast.

Here's a way it could have been:

Johnny flew 2100 miles Miami to SF against the wind while his girl friend flew
from SF to Miama with the wind in 4.8 hours.  They communicated by cell phone
and kept their air speed indicators exactly the same speed the whole way. It
took him 5.6 hours and her 4.8 hours. 

x = air speed (how fast they would be going if the air was still.

         distance    rate      time
Johnny     2100      x-w       5.6 
girl       2100      x+w       4.8

           2100 = (x-w)5.6
           2100 = (x+w)4.8

Multiply the first by 5.6 and the second by 4.8

            375   = x - w
            437.5 = x + w

Add the equations get 

           812.5 = 2x
          406.25 = x

Multiply the first by -1 and add

            -375  = -x + w
            437.5 =  x + w
             52.5 =     2w
            25.25 = w

So the airspeed they kept their planes at was 406.25 mph and
the wind was blowing 25.25 miles per hour toward the west.

That's probably not the way it was stated but at least that
makes a little more sense.

Edwin

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I will rewrite this so it makes sense:
;
Johnny went head wind (east to west I believe) from Miami to San Francisco 2100 miles in 5.6 hours.
When this other person (a girl) went tail wind (west to east) from San Francisco to Miami 2100 miles too but only took 4.8 hours...
:
what is the air speed and the wind speed?
:
Let s = speed in still air
let w = rate of the wind
then
(s-w) = effective speed against the wind
and
(s+w) = effective speed with the wind
;
Write a distance equation for each trip; dist = time * speed
:
5.6(s-w) = 2100
4.8(s+w) = 2100
Simplify this, divide the 1st equation by 5.6 and the 2nd equation by 4.5, resulting in:
s - w = 375
s + w = 437.5
--------------- adding eliminates w, find s
2s = 812.5
s = 812.5/2
s = 406.25 mph is the speed in still air
then
406.25 + w = 437.5
w = 437.5 - 406.25
w = 31.25 mph is the speed of the wind
;
:
You can confirm this by replacing s and w in the original equations and doing the math

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I=0.11x +750

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A jet plane traveling at 500 mph overtakes a propeller plane traveling at 200 mph that had a 2-hour head start. How far from the starting points are the planes?
------
Prop plane DATA:
rate = 200 mph ; time = x hrs ; distance = r*t = 200x miles
------
Jet plane DATA:
rate = 500 mph ; time = x-2 hr ; distance = 500(x-2) miles
-----
Equation:
prop distance = jet distance
---
200x = 500x -1000
300x = 1000
x = 3 1/3 hrs = 3 hrs 20 min
================================
Cheers,
Stan H.
=================

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Sarah drove from Ajax to Bixby at an average speed of 50 mi/h. On the way back, she drove 60 mi/h. The total trip took 4 2/5 hours of driving time. Find the distance between the cities. I tried doing a chart but the answer I got just didnt make sense at all. Word problems are not my fortay.
=========================
Avg speed of a round trip is
2*r1*r2/(r1 + r2) (take my word for it, or I can prove it)
Avg = 2*50*60/(50 + 60) = 600/11 mi/hr
----------------
d = r*t
d = (600/11)*4.4 = 240 miles round-trip
One way = 120 miles

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Plane moving at 90 m/ hour and plane at 116mph they are 2060 miles apart when will they meet
--------------
Which directions are they moving?

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How many hours will it take me to traval 72 miles at 65mph?
-----------
d = r*t
t = d/r

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65/58=1.1207km/m
1.1207km*60=67.2414km/h
1mph=1.6093km/h
(67.2414km/h) / (1.6093km/h)
=41.78mph

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A ferry travels at 15 miles per hour how long does it take the ferry to travel 13.4 miles?
------------
d = r*t
t = d/r

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d = rt

200 = 75t

200/75 = t

8/3 = t

t = 8/3

t = 2.667

So it will take roughly 2.667 hours (or exactly 160 minutes).

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two planes 1350 miles apart are flying toward each other at different altitudes. if one is flying at 250 miles per hour and the other at 290 miles per hour, how long will it take them to pass each other?
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Their closing speed is 250+290 = 540 mph
----
time = distance/rate
time = 1350/540 = 2.5 hrs.
============
cheers,
Stan H.

Their approach rate is 57+63 = 120 floors per minute.  They are 51-11 = 40
floors apart. Since 40 is 1/3 of 120, it'll only take 1/3 of a minute till
their paths cross. So at 57 floors per minute, in 1/3 of a minute, Steve will
go up  1/3 of 57 or 19 floors, so he'll be on the 11th+19 = 30th floor in 1/3
of a minute. That's the answer.  But as a check, at 63 floors per minute, Joyce
will come down 1/3 of 63 or 21 floors, so she'll be on the 51st-21 or 30th
floor too in 1/3 of a minute.  So it checks.

Answer: 30th floor.  

Edwin