# Time, Speed & Distance: At What Speed Should The Man Cycle?

This topic entails solving problems of varying complexity with the help of several equations. There is only one formula and it is known to most of you: Distance = Speed * Time. However, what differentiates one problem from the other is the application of the formula. These problems are more about logic and application.

This basic formula leads to 2 special cases.

Case 1: Distance Constant
If the distance of the journey is constant, then the time taken for travel is inversely proportional to speed.

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=> Time α (1/Speed)
=> T1 / T2 = S2 / S1

So, if the speed of journey is tripled, the time of journey becomes one-thirds.

Case 2: Time Constant

If the time of the journey is constant, then the distance taken for travel is directly proportional to speed.
=> Distance α Speed
=> D1 / D2 = S1 /S2

So, if the speed of journey is doubled, the distance covered for the same time becomes double.

Solve the following question –

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/ hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

(A) 11 Km/hr

(B) 12 Km/hr

(C) 13 Km/hr

(D) 14 Km/hr

(E) 15 Km/hr