A train covered the distance of 400 km between A and B at a certain speed. On the way back it covered 2/5 of the distance at that same speed and then it decreased its speed by 20 km/hour. Find the speed of the train at the end of its journey from B back to A, if the entire trip took 11 hours.

Question

A train covered the distance of 400 km between A and B at a certain speed. On the way back it covered 2/5 of the distance at that same speed and then it decreased its speed by 20 km/hour. Find the speed of the train at the end of its journey from B back to A, if the entire trip took 11 hours.

Answer 1

Most of these distance-rate-time problems are basically the same.

I did the last one for you,
give this one fair try, and let me know at which point you get stuck.

Hint: let the "certain" speed be x km/h
then the slower speed is x-20 km/h

Answer 2

I am really stuck with creating the equation

Answer 3

First part of trip:

distance = 400 km
speed = x km/h
time = d/r = 400/x hrs

return trip
2/5 of 400 at x km/h, then 3/5 of 400 at x-20 km/h
how far did the train go at x km/h ?
how far did the train go at x-20 km/h ?
What is the time for the first part of this return trip?
What is the time for the 2nd part of this return trip

You now have 3 different times
What is the total of these times ???

form you equation.

Answer 4

To solve this problem, let's break it down into steps:

Step 1: Determine the time taken for the train to cover the distance from A to B.

Let's assume the speed of the train from A to B is "x" km/hour. The distance between A and B is 400 km. Using the formula Time = Distance / Speed, we can find the time taken for the train to travel from A to B:

Time1 = Distance1 / Speed1
Time1 = 400 km / x km/hour

Step 2: Determine the time taken for the return journey.

On the return journey, the train covers 2/5 of the distance at the same speed, and then it decreases its speed by 20 km/hour for the remaining distance. Let's calculate the time taken for each part of the return journey:

Time2 = (2/5) * Distance1 / Speed1
Time3 = (3/5) * Distance1 / (Speed1 - 20)

Step 3: Total time taken for the entire trip.

The total time taken for the entire trip is given as 11 hours. Therefore, we can set up the equation:

Time1 + Time2 + Time3 = 11

Step 4: Solve the equation to find the value of the speed.

Substituting the values from Step 1, Step 2, and the given total time into the equation from Step 3, we get:

(400/x) + [(2/5) * (400/x)] + [(3/5) * (400/(x - 20))] = 11

Simplify the equation and solve for x.

Step 5: Once you solve the equation, you will find the value of x, which represents the speed of the train. This will be the speed of the train at the end of its journey from B back to A.