Question

A trains 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?

Answer 1

Speed of first train = 36 mph

Speed of second train = 60 mph

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 =
`x\ mph`

Time of travel between 2:00 PM to 7:00 PM =
`7-2=5\ h`

Distance traveled by 1st train in 5 hours in miles =
`Speed* time = x* 5 = 5x`

Second train:

Then, speed of second train will be =
`(x+24)\ mph`

Time of travel between 4:00 PM to 7:00 PM =
`7-4 = 3\ h`

Distance traveled by second train in 3 hours in miles =
`Speed* time = (x+24)* 3=3x+72`

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:

`5x=3x+72`

Solving for
`x`

Subtracting both sides by
`3x`

`5x-3x=3x-3x+72`

`2x=72`

Dividing both sides by 2.

`(2x)/(2)=(72)/(2)`

∴
`x=36`

Speed of first train = 36 mph

Speed of second train =
`36+24=` 60 mph