SOLUTION: A train travels 110 km in the same time that a plane covers 385km. If the speed of the plane is 20 km per hr less than 4 times the speed of the train, find both speeds.

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Question 994696: A train travels 110 km in the same time that a plane covers 385km. If the speed of the plane is 20 km per hr less than 4 times the speed of the train, find both speeds.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the train in km/hr
+4s+-+20+ = the speed of the plane in km/hr
--------------------
Equation for train:
(1) +110+=+s%2At+
Equation for plane:
(2) +385+=+%28+4s+-+20+%29%2At+
----------------------
(2) +385+=+4s%2At+-+20t+
and
(1) +s+=+110%2Ft+
-----------------
By substitution:
(2) +385+=+4%2A%28+110%2Ft+%29%2At+-+20t+
(2) +385+=+440+-+20t+
(2) +20t+=+55+
(2) +t+=+11%2F4+
+s+=+110%2Ft+
+s+=+110%2A%284%2F11%29+
+s+=+40+
and
+4s+-+20+=+4%2A%28110%2Ft+%29+-+20+
+4s+-+20+=++4%2A110%2A%284%2F11%29+-+20+
+4s+-+20+=+160+-+20+
+4s+-+20+=+140+
-----------------
The speed of the train is 40 km/hr
The speed of the train is 140 km/hr
-----------------
check:
(2) +385+=+%28+4s+-+20+%29%2At+
(2) +385+=+140%2A%2811%2F4%29+
(2) +385+=+385+
and
(1) +110+=+s%2At+
(1) +110+=+40%2A%2811%2F4%29+
(1) +110+=+110+
OK