SOLUTION: A person is travelling by train and car in his whole journey.. The matter is if he is travelling first by train till 60 kms and the rest by car, then his total journey has taken 4
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Question 1011876: A person is travelling by train and car in his whole journey.. The matter is if he is travelling first by train till 60 kms and the rest by car, then his total journey has taken 4 hours.. but if he is travelling first by train till 100 kms, then his journey has taken 10 mins more than before.. According to the question, what was the speed of that train?? Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website! Two arrangements of travel are described. The individual time quantities are not given but overall time quantities are given. Descriptions of rates are not given. Let d be the trip's distance.
Arrangement A
rate time distance
TRAIN R 60
CAR r d-60
Total 4
Arrangement B
rate time distance
TRAIN R 100
CAR r d-100
Total 4&1/6
Fill the missing time slots according to y=mx, x=y/m.
Arrangement A
rate time distance
TRAIN R 60/R 60
CAR r (d-60)/r d-60
Total 4
Arrangement B
rate time distance
TRAIN R 100/R 100
CAR r (d-100)/r d-100
Total 4&1/6
Note that 10 minutes is of an hour.
You have two time-sum equations to make. The system of equations is .
Do you see ANYTHING else? MAYBE the time difference of the two arrangements?
A few steps of work on this time difference equation gives simplified
Return now to the system of two equations with the three variables, r, R, d, and solve each of them for d; and then equate the expressions! I will not include showing those steps here, but you may get an equation consistent with
or
You have from this another system of two equations in just r and R: .
(