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?

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)   (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 RETURN b d TOTAL t 2d

The obvious equation to make is and the only unknown variable is d, the variable which needs to be solved for.
Answer by ikleyn(52786)   (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: + = 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 is the time of driving at the speed of 30 mph, while 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 = miles = miles. Check. : = ; : = ; = = = = = 0.5. Correct!

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the one-way distance to work
Let = time in hrs to get to work
= time in hrs to get home from work
( note that I converted min to hrs )
------------------------------------
Driving to work:
(1)
Driving home:
(2)
-------------------------
Plug (1) into (2)
(2)
(2)
(2) hrs
and
(1)
(1)
(1) mi
Work is 8.08 mi away
-----------------------
check answer:
(2)
(2)
(2)
(2)
close enough

Answer by Alan3354(69443)   (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
=========================
The formula for avg speed of a RT (or 2 legs of equal length) is similar to parallel resistances or parallel work.

RELATED QUESTIONS
You drive at an average of 30 miles per hour on the way to work, and at an average of 35... (answered by Alan3354)
Traveling at an average speed of 60 miles per hour can give better gas mileage than... (answered by ankor@dixie-net.com)
Traveling at an average speed of 60 miles per hour can give better gas mileage than... (answered by scott8148)
You walk at an average of 3.2 miles per hour on the way to school, and at an average of 4 (answered by ankor@dixie-net.com)
in the morning you traveled at an average speed of 25 miles per hour (mph) to get to... (answered by ankor@dixie-net.com)
driving to your friends house, you travel at an average rate of 35 miles per hour. on... (answered by josgarithmetic)
Driving to your friend's house, you travel at an average rate of 35 miles per hour. On... (answered by josgarithmetic)
You bike 50 miles from home. On your way back, your average speed increases by 3 miles... (answered by josmiceli)
A car travels an average speed of 70 miles per hour, on the way back the average speed... (answered by Alan3354)