A train leaves Boston at 4:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 84mph84mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?
Question
A train leaves Boston at 4:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 84mph84mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains?
Solution
Step 1: Determine the time each train has been traveling when the second train overtakes the first.
The first train leaves at 4:00 PM and is overtaken at 10:00 PM, so it has been traveling for 6 hours.
The second train leaves at 8:00 PM and overtakes the first at 10:00 PM, so it has been traveling for 2 hours.
Step 2: Set up an equation to represent the distances each train has traveled.
Since distance = speed x time, and both trains have traveled the same distance when the second one overtakes the first, we can set up the following equation:
Speed of first train x 6 hours = (Speed of first train + 84 mph) x 2 hours
Step 3: Solve the equation for the speed of the first train.
Solving the equation gives us the speed of the first train = 42 mph.
Step 4: Determine the speed of the second train.
Since the second train travels 84 mph faster than the first, its speed is 42 mph + 84 mph = 126 mph.
So, the first train travels at 42 mph and the second train travels at 126 mph.
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