Need help with question fast! Thanks!

Question

The sum of the speeds of two trains is 721.8 miles per hour. If  the speed of the first train is 10.2 mph faster than the second train, find the speeds of each.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the variables to one another. On this one we have

x + y = 721.8   because the sum between them is 721.8

x = y + 10.2    because the speed of the first train is 10.2 mph faster

from there then I would plug in the second equation into the first and then solve algebraically

y + 10.2 + y = 721.8

2y = 711.6

y = 355.8

meaning that x = 355.8 + 10.2 = 366

so the speed of the first train is 366 mph and the speed of the second train is 355.8 mph

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Alrighty, so if the sum of the speeds of two trains in 721.8 mph, that means that (1) Train 1 + Train 2 = 721.8 mph.

 

Using the given information, we know that Train 1 is 10.2 mph faster than Train 2 ... This means that Train 1 travels at 10.2 times Train 2, or in other words (2) 10.2*Train 2 = Train 1. We can now plug this into equation (1) to solve for the speed of Train 2.

 

10.2*Train 2 + Train 2 = 721.8

Train 2 = 721.8 / 11.2 = (about) 64.45 mph

 

Plugging this value of Train 2 into equation (2)

 

10.2*Train 2 = Train 1

10.2 * 64.45 = (about) 657.39 mph

 

Thus, Train 1's speed is 657.39 and Train 2's is 64.45 mph.

 

We can check this by making sure 657.39 + 64.45 = 721.84 (which is only 0.04 off from 721.8).

Your answer will differ depending on how many digits you round to.

 

Hope this helps!