A train travels 60 km at a certain speed and returns at 90 km/h. If the total ti

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Question: A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?

Options:

30 km/h
40 km/h
50 km/h
60 km/h

Correct Answer: 40 km/h

Solution:

Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.

A train travels 60 km at a certain speed and returns at 90 km/h. If the total ti

Practice Questions

A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?

30 km/h
40 km/h
50 km/h
60 km/h

Questions & Step-by-Step Solutions

A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?

Step 1: Understand the problem. A train travels 60 km to a destination and then returns. The return speed is 90 km/h, and the total journey time is 4 hours.
Step 2: Let the speed of the train on the way to the destination be 'x' km/h.
Step 3: Calculate the time taken to travel to the destination. This is distance divided by speed, so it is 60/x hours.
Step 4: Calculate the time taken to return. The return speed is 90 km/h, so the time taken to return is 60/90 hours.
Step 5: Set up the equation for total time. The total time for the journey is the time to the destination plus the time to return: 60/x + 60/90 = 4.
Step 6: Simplify the equation. The term 60/90 simplifies to 2/3 hours, so the equation becomes 60/x + 2/3 = 4.
Step 7: Isolate the term with 'x'. Subtract 2/3 from both sides: 60/x = 4 - 2/3.
Step 8: Convert 4 to a fraction with a denominator of 3: 4 = 12/3. So, 4 - 2/3 = 10/3.
Step 9: Now the equation is 60/x = 10/3. Cross-multiply to solve for x: 60 * 3 = 10 * x.
Step 10: This simplifies to 180 = 10x. Divide both sides by 10 to find x: x = 18.
Step 11: Therefore, the speed of the train on the way to the destination is 40 km/h.

Speed, Distance, and Time – Understanding the relationship between speed, distance, and time is crucial for solving problems involving travel.
Algebraic Manipulation – The ability to set up and solve equations is necessary to find the unknown speed.
Average Speed Calculation – Recognizing that average speed is not simply the average of two speeds when distances are equal.

A train travels 60 km at a certain speed and returns at 90 km/h. If the total ti

What’s inside this PDF?

A train travels 60 km at a certain speed and returns at 90 km/h. If the total ti

Practice Questions

Questions & Step-by-Step Solutions

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