SOLUTION: A train runs 224km between 2 cities. If the speed on the way back is 8km/h slower, the run takes half an hour longer. Determine the speed on the way back.

Question 691629: A train runs 224km between 2 cities. If the speed on the way back is 8km/h slower, the run takes half an hour longer. Determine the speed on the way back.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = time in hrs for 1st trip
= time in hrs for 2nd trip
Let = speed in km/hr for 1st trip
= speed in km/hr for 2nd trip
-----------------------------------
1st trip:
(1)
2nd trip:
(2)
---------------------------
(2)
and
(1)
Substitute (1) into (2)
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
I'll complete the square
(2)
(2)
(2)
(2)
(2)
(2)
(2) ( ignore the negative square root of )
and

The train's speed on the way back is 56 km/hr
check answer:
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
(1)
OK

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