SOLUTION: If Sandra drove to work at 30 mph, she will be late by 15 minutes. If she drove at 40 mph, she will arrive 10 minutes early. How far does she travel in going to work?

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Question 1115466: If Sandra drove to work at 30 mph, she will be late by 15 minutes. If she drove at 40 mph, she will arrive 10
minutes early. How far does she travel in going to work?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let L be the distance to work.


Then from the condition you have this "time" equation


L%2F30 - L%2F40 = 1%2F4 + 1%2F6.


Multiply both sides by 120. You will get


4L - 3L = 30 + 20,   or


L = 50.


Answer.  50 miles.


Check.  50%2F30+-+50%2F40 = 5%2F3+-+5%2F4 = 20%2F12-15%2F12 = 5%2F12;   1%2F4+%2B+1%2F6 = 3%2F12+%2B+2%2F12 = 5%2F12.   ! Correct !

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Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x, time normally expected
d, distance to work 
SPEED       TIME            DISTANCE
30         t%2B1%2F4           d
40         t-1%2F6           d


30%28t%2B1%2F4%29=40%28t-1%2F6%29
-
3%28t%2B1%2F4%29=4%28t-1%2F6%29
3t%2B3%2F4=4t-2%2F3
t=3%2F4%2B2%2F3
t=17%2F12

-
DISTANCE
30%2817%2F12%2B1%2F4%29
30%2817%2F12%2B3%2F12%29
30%2A20%2F12
highlight%2850%29