Question

A man reaches 5 minutes early if he rides at a speed of 50 km per hour. But he would be 10 minutes late if he rides at a speed of 40 km per hour. What is the distance to be covered by the man?

Answer 1

To find the distance a man must cover, create equations based on travel times at 50 km/h and 40 km/h, then solve for distance, ensuring the answer's reasonableness by checking the time difference.

Step-by-step explanation:

To calculate the distance that a man must cover on his journey, we can use the information provided regarding his arrival times at different speeds. When he travels at 50 km/h, he arrives 5 minutes early, and when he goes at 40 km/h, he arrives 10 minutes late. This implies that the time difference when traveling at these two different speeds is 15 minutes, or 0.25 hours.

We can set up two equations based on the speeds and times: Time at 50 km/h = (Distance / 50 km/h) - 5 minutes, Time at 40 km/h = (Distance / 40 km/h) + 10 minutes. After converting minutes to hours and setting these two equations equal to each other (since they essentially describe the time for the same trip), we can solve for the distance.

Checking the reasonableness of the answer is an important step, which in this case would be confirming that the distance calculated, when divided by the speeds given, would result in a time difference of 15 minutes. The exact calculations are not provided here, but a student should be able to carry them out using the above setup to find the required distance.