SOLUTION: An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route

Question 1154641: An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was
3 1/2 hours. If the train traveled 10 mph slower with the tank cars full, how fast did the train travel in each direction? thanks
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.

Let x be the slower speed, in miles per hour. Then the faster speed is (x+10) mph. The "time" equation is + = hours. To solve it, multiply both sides by 2x*(x+10). Then reduce to the standard form quadratic equation and solve it by any way you want/you like. ANSWER. The speeds are 40 mph and 30 mph. (You may solve it MENTALLY (!) )

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = rate with tank empty
rate with tank full
Let = time in hrs with tank empty
= time with tank full
---------------------------------------------
With tank empty:
(1)
With tank full:
(2)
----------------------------------------
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)

too slow
---------------------------

The train's speed with tank empty was 40 mi/hr
The train's speed with tank full was 30 mi/hr
--------------------------------------------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK

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