Atrains leaves cincinnati at 2: 00 pm. a second train leaves the same station in the same direction at 4: 00 pm. the second train travels 24 mph faster than the first. if the second train overtakes the first at 7: 00 pm, what is the speed of each train?

Speed of first train = 36 mph

Speed of second train =  60 mph

Step-by-step explanation:

Given:

First train leaves Cincinnati at 2:00 PM

Second train leaves same station at 4:00 PM

Speed of second train is 24 mph faster than first train.

The second train overtakes the first at 7:00 PM

To find the speeds of each train.

Solution:

First train:

Let speed of first train be =

Time of travel between 2:00 PM to 7:00 PM =

Distance traveled by 1st train in 5 hours in miles =

Second train:

Then, speed of second train will be =

Time of travel between 4:00 PM to 7:00 PM =

Distance traveled by second train in 3 hours in miles =

At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.

Thus, we have:

Solving for

Subtracting both sides by

Dividing both sides by 2.

∴

Speed of first train = 36 mph

Speed of second train = 60 mph

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step-by-step explanation: