Question

A certain distance is covered at a certain speed. If half the distance is covered in double the time, what is the ratio of the two speeds?

• A. 3 : 2
• B. 2 : 1
• C. 4 : 1
• D. 1 : 3

Answer 1

Answer:

C. 4 : 1

Understanding the Concepts

• Speed, Distance, and Time: Speed is directly proportional to distance when time is constant. Speed is inversely proportional to time when the distance is constant.

Setting up the Problem

• Let the original distance be 'd' and the original speed be 's'.

• In the first scenario, the time taken ($t_1$) can be calculated as: $t_1$ = d/s

• In the second scenario:

  • Distance = d/2

  • Time = 2 $t_1$ = 2 (d/s) = 2d/s

  • Let the new speed be '$s_2$'

Calculating the New Speed ($s_2$)

• $s_2$ = (d/2) / (2d/s) = s/4

Finding the Ratio of Speeds

• Ratio of original speed (s) to new speed (s2): s / (s/4) = 4/1

Therefore, the ratio of the two speeds is 4:1.