Problema Solution
A train left Moscow for the Far East, going at 40 km per hour. A day later another train departed in the same direction going at 45 km per hour. How many days will it take the second train to catch up to the first if the trains do not change their speeds and do not stop?
Answer provided by our tutors
Let
v1 = 40 km/h the speed of the first train
v2 = 45 km/h the speed of the second train
t = the time of the second train in hours
t + 24 = the time of the first train in hours (the first train left 1 day = 24 hours earlier)
Also we know that distance = speed*time.
When the second train catches up the first we have the following equation:
v1*(t + 24) = v2*t (the distance that the first train traveled equals the distance the second train traveled)
Plug the values into the last equation and solve for t:
40(t + 24) = 45t
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click here to see the equation solved for t
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t = 192 hr
t = 192/24 days
t = 8 days
The second train will need 8 days to catch up the first train.