SOLUTION: A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per

Question 29239: A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per hour. How long will it take for the second train to overtake the first train?
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
A train leaves a city heading west and travels at 50 miles per hour. Three hours later, a second train leaves from the same place and travels in the same direction at 65 miles per hour. How long will it take for the second train to overtake the first train?
Let the second train catch up with the first train at Point A,
t hours after it (second train) starts from the city.
The first train travels at 50 miles per hour.
In 1 hour the first train travels 50 miles.
Therefore in 3 hours the train travels (3X50)= 150 miles
And in another t hours it will travel (tX50) = 50 t miles
Total distance travelled by the first train to
reach station A is = (150+50t) miles
The second train travels at 65 miles per hour.
In 1 hour it travels 65 miles.
Therefore in t hours it travels (65t) miles and reaches station A.
Therefore distance from the city to the station A is
65t =(150+50t)
65t-50t =150
15t = 150
t = 10 hours.
Verification: Distance travelled by the first tran in (3+t) hours that is in (3+10) hours is 50X13=650 miles
Distance travelled by the second tran in (t) hours that is in (10) hours is 65X10=650 miles
(that is if the first train leaves at 8AM,the second train leaves at (8+3) = 11AM and the second train catches up with the first train and surges ahead t hours after its start -means it will start overtaking the first train t hours after 11 that is at(11+t) O’clock.)
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