A train leaves Atlanta at 1:00 PM. A second train leaves the same city in the same direction at 5:00 PM. The second train travels 48mph faster than the first. If the second train overtakes the first at 9:00 PM, what is the speed of each of the two trains?
Answers
Answer:
48mph and 96 mph
Step-by-step explanation:
/* Define x */
Let x be the speed of the first train.
The speed of the second train is (x + 48) mph
/* Time taken by the first train */
Duration from 1.00pm to 9.00 pm = 8 hours
/* Time taken by the second train */
Duration from 5.00pm to 9.00 pm = 4 hours
/* Distance = Speed x Time Taken */
/* Distance traveled by the first train */
Speed = x mph
Time Taken = 8 hours
Distance = 8x miles
/* Distance = Speed x Time Taken */
/* Distance traveled by the second train */
Speed = (x + 48) mph
Time Taken = 4 hours
Distance = 4(x + 48) mph
/* Since the trains met at 9pm. the distance traveled by both train at 9pm were the same */
4(x + 48) = 8x
4x + 192 = 8x
4x = 192
x = 48
/* Speed of the first train is x */
Speed of the first train = x = 48 mph
/* Speed of the second train is x + 48 */
Speed of the second train = x + 48 = 48 + 48 = 96 mph
Answer: Speed of the first train is 48 mph and the second train is 96 mph