7) Walking at 5/6 of its usual speed, a train is 10 minutes too late. Find its usual time to cover the journey.

Let's denote the usual speed of the train as S (in km/h), and the usual time it takes to cover the journey as T (in hours).

Step 1: Understand the problem The train is walking at 5/6 of its usual speed, which means the speed is 5S/6. Because speed is inversely proportional to time (the slower the speed, the longer the time), the time it takes at this slower speed is the inverse of 5/6, which is 6/5. So, the time it takes at this slower speed is 6T/5.

Step 2: Set up the equation According to the problem, this slower time is the usual time T plus an additional 10 minutes. We need to remember to convert these 10 minutes to hours, since our time T is in hours. 10 minutes is 10/60 = 1/6 hours. So, we can set up the following equation: 6T/5 = T + 1/6.

Step 3: Solve the equation To solve for T, we first multiply every term by 5 to get rid of the fraction: 6T = 5T + 5/6. Then, we subtract 5T from both sides to get T = 5/6.

So, the usual time for the train to cover the journey is 5/6 hours, which is 50 minutes.