Question 1189686: If I drive 60 mph and arrive 4 minutes late how fast do I have to drive to arrive on time?
Found 3 solutions by ikleyn, ankor@dixie-net.com, Theo:
Answer by ikleyn(52832)   (Show Source):
You can put this solution on YOUR website! .
As worded, printed, posted and presented, this post is incomplete.
It missed some essential part of information, and in this form the problem can not be solved.
As I understand, you heard somewhere about this class of problems and try to invent / (to compose) on your own,
but have no enough knowledge to do it correctly.
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At this forum, I teach how to solve problems, but I DO NOT TEACH how to create them - - -
- - - because skills to compose require, as a pre-requisite, knowledge on solving problems, which you do not have.
It is the same as in music : you can not compose for piano, if you can not play piano . . .
Answer by ankor@dixie-net.com(22740)  (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let r = rate
let t = time
let d = distance
when rate = 60 and time = t + 4/60 and distance = d, the formula becomes:
60 * (t + 4/60) = d
since the time is in hours, then 4 minutes late is 4/60 hours late.
that's why the time is equal to (t + 4/60).
simplify this to get:
60t + 60*4/60 = d
simplify further to get:
60t + 4 = d
solve for t to get:
t = (d-4)/60
go back to your basic formula of rate * time = distance
when rate = r and time = (d-4)/60 and distance = d, you get:
r * (d-4)/60 = d
solve for r to get:
r = 60d / (d-4)
you have one equation with two unknowns.
you will not be able to solve this for a unique value.
the best you can do is solve for the rate in terms of the distance.
you will get a different rate, depending on the distance.
if the distance is 10 miles, then the formula becomes:
r = 60 * 10 / 6
solve for r to get:
r = 100 miles per hours.
if the distance is 50 miles, then the formula becomes:
r = 60 * 50 / 46
solve for r to get:
r = 65.2173913 miles per hour.
if the distance is 100 miles, then the formula becomes:
r = 60 * 100 / 96
solve for r to get:
r = 62.5 miles per hour.
if the distance is 200 miles, then the formula becomes:
r = 60 * 200 / 196
solve for r to get:
r = 61.2244898 miles per hour.
if the distance is 300 miles, then the formula becomes:
r = 60 * 300 / 296
solve for r to get:
r = 60.81081081
if the distance is 400 miles, then the formula becomes:
r = 60 * 400 / 396
solve for r to get:
r = 60.60606061.
the equation can be graphed as shown below:
in the graph, y takes the place of r and x takes the place of d.
the coordinate points are in (x,y) format.
x is the distance
y is the rate
let me know if you have any questions.
theo
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