SOLUTION: A freight train travels 60 km. A single locomotive pulls the train for the first half of the trip, then a second locomotive is added, doubling the speed of the train. If the total
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Question 1151413: A freight train travels 60 km. A single locomotive pulls the train for the first half of the trip, then a second locomotive is added, doubling the speed of the train. If the total time for the trip is 54 min, what is the speed of the train with one locomotive. Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52858) (Show Source):
Let x be the train's speed under the question.
Then the time equation is
+ = .
Multiply both sides by 60x. you will get
1800 + 900 = 54x
2700 = 54x
x = 2700/54 = 50.
ANSWER. 50 km/h.
Here is a non-algebraic way to solve the problem using logical reasoning and some mental arithmetic.
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.
With the one locomotive, 30km in 36 minutes (3/5 of an hour) makes the speed in km/hr with one locomotive
ANSWER: The speed of the train with one locomotive is 50km/hr.
