SOLUTION: You commute 56 miles one way to work. The trip takes 10 minutes longer than the trip home.your average speed on the trip home is 8 miles per hour faster. What is your average speed

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Question 648064: You commute 56 miles one way to work. The trip takes 10 minutes longer than the trip home.your average speed on the trip home is 8 miles per hour faster. What is your average speed on the trip home?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Average speed on trip home is
( distance in miles ) / ( time in hrs )
Let +t+ = the time in hours going home
+t+%2B+10%2F60+ = time to go to work
+56+%2F+%28+t+%2B+1%2F6+%29+ = speed going to work
+56+%2F+t+ = speed going home
-------------------
given:
+56+%2F+t+=+56+%2F+%28+t+%2B+1%2F6+%29+%2B+8+
Multiply both sides by +t%2A%28+t+%2B+1%2F6+%29+
+56%2A%28+t+%2B+1%2F6+%29+=+56t+%2B+8t%2A%28+t+%2B+1%2F6+%29+
+56t+%2B+28%2F3+=+56t+%2B+8t%5E2+%2B+4t%2F3+
Subtract +56t+ from both sides
and multiply both sides by +3+
+28+=+24t%5E2%2B+4t+
+6t%5E2+%2B+t+-+7+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+6+
+b+=+1+
+c+=+-7+
+t+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A6%2A%28-7%29+%29%29+%2F+%282%2A6%29+
+t+=+%28-1+%2B-+sqrt%28+1+%2B+168+%29%29+%2F+12+
+t+=+%28-1+%2B-+sqrt%28+169+%29%29+%2F+12+
+t+=+%28+-1+%2B+13+%29+%2F+12+
+t+=+1+
+56+%2F+t+ = average speed going home
+56%2Ft+=+56+
The average speed going home is 56 mi/hr
check:
+56+%2F+%28+t+%2B+1%2F6+%29+ = speed going to work
+56+%2F+%287%2F6%29+=+48+ mi/hr
rate x time = +48%2A%28+t+%2B+1%2F6+%29+
+48%2A%287%2F6%29+=+56+ mi
OK