I need someone to help me with math problems and explain them to me Please Help?

Question

If a woman drives from home straight to work at an average speed of 480/13 mph., she arrives at work 1 minute late. However, if the woman drives from here home straight to work at an average speed of 40mph., she arrives at work 1 minute early. Find the number of miles from the woman's house straight to work.
Thanks,
Kickgirl91
PS-these math questions are helping me study for math team so I am NOT cheating

Answer 1

we know that speed = distance/time

let us say that the women takes t minutes to travel to work at 40 milesper hour
40 mph= 0.6666 miles per minute {1 hr = 60 min}{ie:40/60}
similarly at 480/13 mph she takes t + 2 minutes{ie 2 min extra}
480/13 mph = 0.6154 miles per minute{ie 480/13/60}
as the distance she travells at both speeds are the same, two distance equations are formed as follows:
distance = speed * time
at 40 mph:
distance = .6666t
at 480/13 mph:
distance = .6154(t+2)
ie : distance = .6666t = .6154(t + 2)
solving we get
t = 24.039 minutes
now distance = .6666t =.6666 * 24.039 =16.024 miles
hope this helps u

Answer 2

This is a problem involving time, distance and speed. Usually, when you are given any two of these things, you can find the third one.

Speed = distance / time

In this case, you are given one item, but in two different contexts.

So we'll have two equations with two unknowns: t for time and d for distance. In this case, t is in hours (or fraction of hour) and d will be in miles -- that's because we are given speeds in miles per hour.

Case 1:

480/13 = d / (t + 1/60)

At a speed of 480/13, the distance d is covered in a time that is 1 minute more than the ideal time t. 1 minute is 1/60 of an hour

Case 2:

40 = d / (t - 1/60)

rewrite both equations by moving the time portion to the other side (we multiply both sides by the time element.

(1) (t + 1/60) * 480/13 = d

(2) (t - 1/60) * 40 = d

We now have two equations where a different arrangement is equal to the same d; they are therefore equal to each other:

(3) (t + 1/60) * 480/13 = (t - 1/60) * 40

From then on, you have an equation with only one unknown "t"

Answer 3

Let t = time to drive to work
Then (480/13)(t+1) =distance to school
And 40(t-1) = distance to school
Thus (480/13)(t+1) = 40(t-1)
(480/13)t + 480/13 = 40t - 40
(480/13)t -40t = -40 - 480/13

[(480 -520)/13]t = (-520-480)/13
-40t = - 1000
t = 25 minutes