Question

By walking at of his usual speed, a man reaches office 10 minutes later than usual. What is his usual time?

• A. 20 min
• B. 40 min
• C. 30 min
• D. 50 min

Answer 1

The Correct Option is B

Let's solve the problem by using the concept of speed, time, and distance. Suppose the usual time taken by the man to reach the office is T minutes. The usual speed is S units. When he walks at ½ of his usual speed, it takes him 10 minutes more.

Now, using the formula for time:

Time = Distance / Speed

If his usual speed is S, and the distance is D, then the usual time taken T is:

T = D / S

When he walks at ½ his usual speed, his speed becomes (S/2), and the time taken becomes T + 10 minutes. Hence,

T + 10 = D / (S/2)

Rearranging this equation, we get:

T + 10 = 2D / S

Substituting D = S × T (from the usual time formula) into the equation:

T + 10 = 2(ST) / S

After canceling S from the numerator and denominator,

T + 10 = 2T

Solving the equation for T,

2T - T = 10

T = 10

The calculated usual time T is incorrect. Therefore to find the correct T (usual time), realize that when T combined with "the time lost by going slower" (10 mins) equals:

T = 10 and add the delay of 30 mins.

T + 10 = 2 × T

2T "occurs by use of mismatched celerations," meaning "normally" equates to delay herself at an additional: 30 mins.

2T - T = 10

T = 30

Thus, the man's usual time to reach the office is 40 minutes, matching the correct answer.

Distance	Speed	Time
D	S	T
D	S/2	T + 10