SOLUTION: You drive at an average of 30 miles per hour on the way to work, and at an average of 35 miles per hour on the way home. The total driving time is 30 minutes. How far away is work?

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Question 1046151: You drive at an average of 30 miles per hour on the way to work, and at an average of 35 miles per hour on the way home. The total driving time is 30 minutes. How far away is work? Round your answer to the nearest hundredth of a mile.
Found 4 solutions by josgarithmetic, ikleyn, josmiceli, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
KNOWN:
g, rate going to work
b, rate returning from work
t, total driving time in HOURS
UNKNOWN:
d, distance between home and work

Travel Rates Rule, RT=D to relate rate, time, distance 
               SPEED       TIME       DISTANCE
GOING            g                      d
RETURN           b                      d
TOTAL                       t          2d

Two time cells are not filled but they can be so using the basic travel rate rule. 
               SPEED       TIME       DISTANCE
GOING            g         d%2Fg          d
RETURN           b         d%2Fb          d
TOTAL                       t          2d

The obvious equation to make is highlight%28d%2Fg%2Bd%2Fb=t%29 and the only unknown variable is d, the variable which needs to be solved for.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
You drive at an average of 30 miles per hour on the way to work, and at an average of 35 miles per hour on the way home.
The total driving time is 30 minutes. How far away is work? Round your answer to the nearest hundredth of a mile.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Normally you should write the basic equation at once:

D%2F30 + D%2F35 = 0.5,

where D is an unknown distance in miles, 0.5 is the time of 30 minutes in hours.

By writing this equation, you should understand that D%2F30 is the time of driving at the speed of 30 mph, 
while D%2F35 is the time of driving at the speed of 35 mph.

To solve the equation, multiply both sides by 30*35 to rid off the denominators. You will get

35*D + 30*D = 0.5*30*35,   or

65*D = 0.5*30*35,   or   (canceling the factor 5 in both sides)

13*D = 15*7,  and then

D = 105%2F13 miles = 81%2F13 miles.

Check.  81%2F13 : 30 = 105%2F%2813%2A30%29;
        81%2F13 : 35 = 105%2F%2813%2A35%29;
        
        105%2F%2813%2A30%29+%2B+105%2F%2813%2A35%29 = %28105%2A35+%2B+105%2A30%29%2F%2813%2A30%2A35%29 = %28105%2A5%287%2B6%29%29%2F%2813%2A30%2A35%29 = %28105%2A5%29%2F%2830%2A35%29 = %283%2A5%29%2F30 = 0.5.     Correct!


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance to work
Let +t+ = time in hrs to get to work
+.5+-+t+ = time in hrs to get home from work
( note that I converted min to hrs )
------------------------------------
Driving to work:
(1) +d+=+30t+
Driving home:
(2) +d+=+35%2A%28+.5+-+t+%29+
-------------------------
Plug (1) into (2)
(2) +30t+=+17.5+-+35t+
(2) +65t+=+17.5+
(2) +t+=+.26923+ hrs
and
(1) +d+=+30t+
(1) +d+=+30%2A.26923+
(1) +d+=+8.077+ mi
Work is 8.08 mi away
-----------------------
check answer:
(2) +d+=+35%2A%28+.5+-+t+%29+
(2) +8.077+=+35%2A%28+.5+-+.26923+%29+
(2) +8.077+=+17.5+-+9.4231+
(2) +8.077+=+8.0769+
close enough

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You drive at an average of 30 miles per hour on the way to work, and at an average of 35 miles per hour on the way home. The total driving time is 30 minutes. How far away is work? Round your answer to the nearest hundredth of a mile.
---------
Avg speed of the round-trip is
2*30*35/(30+35) = 2100/65 mi/hr = 420/13 mi/hr
------
RT distance = (420/13)*0.5 = 210/13 miles.
Each way = 105/13 = 8.08 miles
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The formula for avg speed of a RT (or 2 legs of equal length) is similar to parallel resistances or parallel work.