Question

A train leaves Miami at 3:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 145 mph faster than the first. Of the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains

Answer 1

Answer:

The first train travels at 58 mph and the second train travels at 203 mph.

Step-by-step explanation:

The first train left Miami at 3:00 PM.

The second train left Miami at 8:00 PM.

Let the speed of the first train be x.

The second train travels 145 mph faster than the first, that is 145 + x

The second train overtakes the first at 10:00 PM

This means that at 10:00 PM, they were both at the same location.

That is 7 hours after the first train left and 2 hours after the second train left.

Speed is given as:

s = d / t

where d = distance traveled and t = time taken

For the first train, after 7 hours traveling at speed x:

x = d / 7

=> d = 7x _______(1)

For the second train, after 2 hours, traveling at speed 145 + x:

145 + x= d / 2

=> d = 290 + 2x ____(2)

Equating (1) and (2):

7x = 290 + 2x

=> 7x - 2x = 290

5x = 290

=> x = 290/5 = 58 mph

Therefore, the first train travels at 58 mph and the second train travels at 203 mph (58 + 145)