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

Answer:

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 = $x\ mph$

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 = $Speed\times time = x\times 5 = 5x$

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 = $Speed\times time = (x+24)\times 3=3x+72$

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.

$\frac{2x}{2}=\frac{72}{2}$

∴ $x=36$

Speed of first train = 36 mph

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