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### Converting Seconds to MPH

```
Date: 07/11/2000 at 19:54:16
From: Bob
Subject: Seconds to MPH conversion CHART

I'm looking for a chart that converts seconds traveled to miles per
hour.  I saw something in an FAQ about dividing by 3600. Thanks.
```

```
Date: 07/12/2000 at 12:07:54
From: Doctor Rick
Subject: Re: Seconds to MPH conversion CHART

Hi, Bob.

Could you specify the problem more carefully? You can't compute a
speed (miles per hour) from a time (seconds) alone. Do you want,
perhaps, times in seconds across the top and distances in feet down
the side? Then the (average) speed is the distance divided by the
time, and we need to convert feet to miles and seconds to hours. The
division by 3600 converts seconds to hours; we similarly need to
divide the distance in feet by 5280 to get the distance in miles. The
whole formula for the problem as I stated it is

D = distance in feet
T = time in seconds
S = speed in miles per hour

S = (D/5280)/(T/3600)
= (D/T)*(3600/5280)
= (15/22)D/T

You can use this formula in a spreadsheet to generate a table with the
ranges of times and distances of interest to you. For instance, in
Excel, a formula like

=15/22*\$B3/C\$2

can be used to generate a table like

1      2      3      4      5      6      7
-------------------------------------------------------------
1   0.682  0.341  0.227  0.170  0.136  0.114  0.097
2   1.364  0.682  0.455  0.341  0.273  0.227  0.195
3   2.045  1.023  0.682  0.511  0.409  0.341  0.292
4   2.727  1.364  0.909  0.682  0.545  0.455  0.390
5   3.409  1.705  1.136  0.852  0.682  0.568  0.487
6   4.091  2.045  1.364  1.023  0.818  0.682  0.584
7   4.773  2.386  1.591  1.193  0.955  0.795  0.682
8   5.455  2.727  1.818  1.364  1.091  0.909  0.779
9   6.136  3.068  2.045  1.534  1.227  1.023  0.877
10  6.818  3.409  2.273  1.705  1.364  1.136  0.974
11  7.500  3.750  2.500  1.875  1.500  1.250  1.071
12  8.182  4.091  2.727  2.045  1.636  1.364  1.169
13  8.864  4.432  2.955  2.216  1.773  1.477  1.266
14  9.545  4.773  3.182  2.386  1.909  1.591  1.364
15  10.227 5.114  3.409  2.557  2.045  1.705  1.461
16  10.909 5.455  3.636  2.727  2.182  1.818  1.558

where the numbers across the top are seconds and the numbers at the
left are feet. Going 11 feet in 3 seconds comes out to 2.5 miles per
hour.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 07/12/2000 at 12:16:22
From: Doctor Twe
Subject: Re: seconds to MPH conversion CHART

Hi Bob! Thanks for writing to Dr. Math!

Unfortunately, seconds measures time and mph measures speed, so unless
can't convert seconds to mph. To convert seconds to hours, we divide
by 3600 - that's where that number comes in.

Let's say, for example, that we were measuring sprinters' times in the
100-yard dash and wanted to convert them to mph. We now have a fixed
distance (100 yards), so we can calculate the speed. Let's say the
sprinters ran it in 4.4 s, 4.6 s, 4.85 s and 5.2 s.

s = d / t

where: s = speed
d = distance
t = time

So for the first sprinter, we have:

s1 = 100 yd / 4.4 s
= 22.73 yd/s

Yards per second? Let's convert that to miles per hour. We can
convert yards to miles by dividing by 1760 and, as mentioned above, we
can convert seconds to hours by dividing by 3600. So we have:

s1 = (100 yd / 1760 yd/mi) / (4.4 s / 3600 s/hr)
= 0.0568 mi / 0.00122 hr
= 46.49 mph

Converting each measurement to miles and hours takes extra time. If we
have more of the same calculations to do, we can incorporate the
constants 1760 and 3600 (and even the 100 yds, if it doesn't change)
directly into the formula with a little algebra:

100 yd
----------
1760 yd/mi
s = ----------------
t
---------
3600 s/hr

100 yd     3600 s/hr
= ---------- * ---------
1760 yd/mi       t

360000 mi
= ---------
1760*t hr

s = 204.54/t mph   [or s = 2250/(11*t) mph for more accuracy.]

Using this "condensed" formula, we can quickly convert the other
sprinters' times into speeds:

s2 = 204.54 / 4.6
= 44.47 mph

s3 = 204.54 / 4.85
= 42.17 mph

s4 = 204.54 / 5.2
= 39.34 mph

I hope this helps! If you have any more questions, write back!

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 07/12/2000 at 15:33:50
From: Bob Hubert
Subject: Re: seconds to MPH conversion CHART

Thanks for the answer you provided. I think my question has
complicated the issue. Let me be more specific and you tell me which
formula is best. I thought it would be very simple to locate a chart
in which the math has already been computed.

If you travel 1 mile in 60 seconds, you are traveling 60 miles per
hour. If you travel that mile in 55 seconds, what is your speed in
MPH?

I want a chart that people can carry in their cars so they do not
depend upon their unreliable automobile speedometers. They can use
a watch to time how many seconds it takes to travel from one milepost
to another, then look at this chart to correctly determine their
speed. I'm playing with the numbers and 3600 keeps coming into the
equation. I'm so close but it is driving me a little nuts that I can't
solve this.

Thanks.
```

```
Date: 07/12/2000 at 16:19:12
From: Doctor Rick
Subject: Re: seconds to MPH conversion CHART

Hi, Bob. Thanks for clarifying your question. If you had said "I'm
looking for a chart that converts seconds IT TAKES TO TRAVEL ONE MILE
to miles per hour," both Dr. TWE and I could have saved our effort.

The formula is almost there in my response. Speed is distance divided
by time. If the distance is 1 mile and the time is T seconds, then the
time in hours is T/3600, and the speed is

Speed = (1 mile)/(T/3600 hours)
= 3600/T

That's pretty simple; you just had it upside down. The table looks
like this:

Seconds  MPH
------------
36       100.0
37       97.3
38       94.7
39       92.3
40       90.0
41       87.8
42       85.7
43       83.7
44       81.8
45       80.0
46       78.3
47       76.6
48       75.0
49       73.5
50       72.0
51       70.6
52       69.2
53       67.9
54       66.7
55       65.5
56       64.3
57       63.2
58       62.1
59       61.0
60       60.0
61       59.0
62       58.1
63       57.1
64       56.3
65       55.4
66       54.5
67       53.7
68       52.9
69       52.2
70       51.4
71       50.7
72       50.0
73       49.3
74       48.6
75       48.0
76       47.4
77       46.8
78       46.2
79       45.6
80       45.0
81       44.4
82       43.9
83       43.4
84       42.9
85       42.4
86       41.9
87       41.4
88       40.9
89       40.4
90       40.0
91       39.6
92       39.1
93       38.7
94       38.3
95       37.9
96       37.5
97       37.1
98       36.7
99       36.4
100      36.0
101      35.6
102      35.3
103      35.0
104      34.6
105      34.3
106      34.0
107      33.6
108      33.3
109      33.0
110      32.7
111      32.4
112      32.1
113      31.9
114      31.6
115      31.3
116      31.0
117      30.8
118      30.5
119      30.3
120      30.0
121      29.8
122      29.5
123      29.3
124      29.0
125      28.8
126      28.6
127      28.3
128      28.1
129      27.9
130      27.7
131      27.5
132      27.3
133      27.1
134      26.9
135      26.7
136      26.5
137      26.3
138      26.1
139      25.9
140      25.7
141      25.5
142      25.4
143      25.2
144      25.0

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 07/12/2000 at 17:44:55
From: Doctor Twe
Subject: Re: seconds to MPH conversion CHART

Hi again Bob! Thanks for writing back!

As with the sprinters example, here we have a fixed distance. In this
case, it's even easier than the 100 yards - it's exactly one mile! We
can use the formula I gave previously to construct the chart:

s = d / t

Where: s = speed
d = distance (1 mile)
t = time (in seconds)

Since the time is in seconds, we can convert it to hours by dividing
it by 3600. But dividing the denominator (bottom of the fraction) by
3600 is the same as multiplying the numerator (top of the fraction) by
3600, so we get:

1 mi
s = --------
(t/3600)

1 mi * 3600
= -----------
t

s = 3600/t

So to convert the time (in seconds) it takes to travel 1 mile to speed
in mph, just divide 3600 by the number of seconds. As a chart, we
have:

Time   Speed          Time   Speed          Time   Speed
(s)    (mph)          (s)    (mph)          (s)    (mph)
----   -----          ----   -----          ----   -----
30     120            60      60            90      40
31     116            61      59            91      40
32     113            62      58            92      39
33     109            63      57            93      39
34     106            64      56            94      38
35     103            65      55            95      38
36     100            66      55            96      38
37      97            67      54            97      37
38      95            68      53            98      37
39      92            69      52            99      36
40      90            70      51           100      36
41      88            71      51           101      36
42      86            72      50           102      35
43      84            73      49           103      35
44      82            74      49           104      35
45      80            75      48           105      34
46      78            76      47           106      34
47      77            77      47           107      34
48      75            78      46           108      33
49      73            79      46           109      33
50      72            80      45           110      33
51      71            81      44           111      32
52      69            82      44           112      32
53      68            83      43           113      32
54      67            84      43           114      32
55      65            85      42           115      31
56      64            86      42           116      31
57      63            87      41           117      31
58      62            88      41           118      31
59      61            89      40           119      30

Using the formula above, you can extend this chart as necessary. Note
that at higher speeds, the change in mph per second increases, so the
margin of error also increases.

Personally, I wouldn't put much stock in the reliability of this
method. It relies on the precision of starting and stopping the watch
at the precise moment you pass the mile marker (parallax becomes an
issue), and the accuracy of the distance between the mileposts. Also,
I'm not so sure it's a good idea to try to read your watch while
driving - perhaps a passenger could do this.

I hope this helps. If you have any more questions, write back again.

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Terms/Units of Measurement

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