A metra commuter train leaves Union Station in Chicago at 12 noon. Twp hours later an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3PM the Amtrak train is 10 miles behind the commuter train. How fast is each going?

Question

A metra commuter train leaves Union Station in Chicago at 12 noon. Twp hours later an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3PM the Amtrak train is 10 miles behind the commuter train. How fast is each going?

I don't understand how to solve this.

I only know how to solve it if the problem has the velocity for both.

Please could someone write the equation

Answer 1

let A = speed of Amtrak train

let M=speed of Metro train

so we can write A=M+50

as A is travelling 50 mph faster than M

as there are two unknowns we need another equation

at 3pm distance travelled by A is Ax1 or 1A miles

at 3pm distance travelled by M is Mx3 miles

but A is 10 miles behind M so

3M-10=1A

we now have two equations so we can solve these for A and M.

Answer 2

I solved it got the right answer but what about the 2hours part?

Answer 3

A train leaves the station at 7:00 A.M. traveling west at 80 mi/h. On a parallel track, a second train leaves the station 3 hours later traveling west a 100 mi/h. At what time will the second train catch up with the first? 29

Answer 4

Sure! Let's break down the problem and figure out the equation to solve it.

Let's represent the speed of the Metra train as "M" (in miles per hour) and the speed of the Amtrak train as "A" (in miles per hour).

We know that the Amtrak train is traveling 50 miles per hour faster than the Metra train, so we can express the speed of the Amtrak train as "M + 50".

Now, let's consider the time that has passed since the Metra train left at 12 noon. As the Amtrak train left two hours later, it means the Amtrak train has been traveling for only 1 hour when it is 3 PM. Therefore, the Amtrak train has traveled for 1 hour less than the Metra train.

Now, we also know that at 3 PM, the Amtrak train is 10 miles behind the Metra train.

So, the equation to solve this problem can be expressed as follows:

Distance traveled by the Metra train = Distance traveled by the Amtrak train + 10 miles

Now, let's express these distances in terms of their respective speeds and time:

(Metra train's speed) * (time traveled by the Metra train) = (Amtrak train's speed) * (time traveled by the Amtrak train) + 10 miles

Using these equations and the information we have, we can solve for the speeds of both trains.