If a person walks at 7/6 of the usual speed, then the person reaches the office 15 minutes earlier than usual. What is the usual time in minutes taken to reach the office at the original speed?

Introduction / Context:
This problem combines ratios with the inverse relationship between speed and time for a fixed distance. When speed increases, time decreases in inverse proportion. The question gives the factor by which speed changes and the change in time, and asks you to find the original time taken for the journey.

Given Data / Assumptions:

• Usual time taken to reach the office = T minutes (unknown).
• New speed = (7 / 6) times the usual speed.
• For a fixed distance, time is inversely proportional to speed.
• With higher speed, the person reaches 15 minutes earlier than usual.

Concept / Approach:
Since distance is fixed, Speed * Time is constant. If speed becomes (7 / 6) times, then time becomes (6 / 7) times the original. Let original time be T, then new time is (6 / 7)T. The difference between original and new times equals 15 minutes. This leads to a simple linear equation in T.

Step-by-Step Solution:
Step 1: Let original time = T minutes. Step 2: New speed = (7 / 6) * original speed, so new time = (6 / 7) * T. Step 3: The person reaches 15 minutes earlier, so time saved = T − (6 / 7)T = 15. Step 4: Simplify the difference: T − (6 / 7)T = (1 / 7)T. Step 5: Set (1 / 7)T = 15. Step 6: Solve for T: T = 15 * 7 = 105 minutes.

Verification / Alternative check:
Compute the new time using T = 105 minutes. New time = (6 / 7) * 105 = 90 minutes. The time saved is 105 − 90 = 15 minutes, which matches the information given, so the solution is verified.

Why Other Options Are Wrong:

• 60, 75, and 90 minutes would give smaller time differences than 15 minutes when adjusted by the factor 6 / 7 and therefore do not satisfy the condition.

Common Pitfalls:
A frequent error is to assume the time changes by the same factor as the speed instead of the inverse factor. Another mistake is to set up the equation with reversed ratios. Always remember that for the same distance, speed and time are inversely proportional, so if speed is multiplied by a factor, time is divided by that factor.

Final Answer:
The usual time taken to reach the office is 105 minutes.