Question 1151413
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Here is a non-algebraic way to solve the problem using logical reasoning and some mental arithmetic.<br>
The distances with one locomotive and with two locomotives are the same -- 30km each.
The rates for the two parts of the trip are in the ratio 1:2.
Since the distances are the same and the rates are in the ratio 1:2, the amounts of time at the two speeds are in the ratio 2:1.
A 2:1 ratio of times with a total time of 54 minutes means 36 minutes at the lower rate and 18 minutes at the higher rate.<br>
With the one locomotive, 30km in 36 minutes (3/5 of an hour) makes the speed in km/hr with one locomotive<br>
{{{30/(3/5) = 30*(5/3) = 50}}}<br>
ANSWER: The speed of the train with one locomotive is 50km/hr.<br>