SOLUTION: Every day Tim drives to work. One Monday morning, with heavy traffic, Tim averaged 30 miles per hour on the way in, and 50 miles per hour on the way home. What was Tim�s average sp

Question 157291: Every day Tim drives to work. One Monday morning, with heavy traffic, Tim averaged 30 miles per hour on the way in, and 50 miles per hour on the way home. What was Tim�s average speed for the entire trip?
Is it possible to determine how far Tim drives to work? Explain.

Found 3 solutions by midwood_trail, ptaylor, gonzo:
Answer by midwood_trail(310)   (Show Source): You can put this solution on YOUR website!
Every day Tim drives to work. One Monday morning, with heavy traffic, Tim averaged 30 miles per hour on the way in, and 50 miles per hour on the way home. What was Tim�s average speed for the entire trip?
To find the average speed, we add 30 + 50 and divide by 2.
30 + 50 = 80/2 = 40 miles per hour.
=========================================================
We cannot determine how far Tim drove (in miles) because NO TRAVEL TIME was given for the trip.
I hope this helps.
Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let d= one-way distance; Total distance=2d
Time required to drive in=d/30
Time required to drive home=d/50
Total Time=(d/30+d/50)
(1) Average Speed =(total distance)/(total time)=
Ave Speed=2d/(d/30+d/50) =
Ave Speed=2d/((5d+3d)/150)=
Ave Speed=2d/(8d/150) multiply numerator and denominator by 150/8d:
Ave Speed=(2d*150/8d)/(8d/150*150/8d)=
Ave Speed=300/8=37.5 mi/hr
Now from (1) above, we see that:
Total Distance=(average Speed)*(Total Time) and we know nothing about the time, so we cannot calculate total distance:
If Total Time=1 hr, then Total Distance=37.5 mi
If Total Time=2 hr, then Total Distance=75 mi
etc., etc

Hope this helps--ptaylor

Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!
he traveled x miles at 30 mph and x miles at 50 mph for a total of 2x miles.
since his total time traveling there and back should equal to the sum of his total time getting there and his total time getting back, the equation becomes.
total time = (x/30 + x/50)
total time is also equal to 2x/y where 2x is the total distance there and back and y is the average speed for the total distance there and back.
2x/y must then equal (x/30 + x/50).
we solve the equation x/30 + x/50 = 2x/y.
we multiply both sides by y to get xy/30 + xy/50 = 2x.
we multiply both sides by 150 (common factor) to get 5xy + 3xy = 300x.
we divide both sides by common factor x to get 5y + 3y = 300
we combine like terms to get 8y = 300
we divide both sides by 8 to get y = 37.5
answer is good for any value of x because the x canceled out of the equation.
solving for 2 different values of x taken at random we get the following:
500/30 + 500/50 = 1000/37.5
becomes 16.6666.... + 10 = 26.6666.....
becomes 26.6666....... = 26.6666.......
ok for one value.
any other value could be 5000 (10 x original number.)
166.6666........ + 100 = 266.6666...........
266.6666........ = 266.6666.........
ok for another value.
any other value of x would also satisfy the equation.

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