Question

A car did a journey in t hours. Had the average speed been x kmph greater, the journey would have taken y hours less. How long was the journey?
1. x(t-y)ty
2. x(t-y)ty^-1
3. x(t-y)ty-2
4. x(t+y)ty

Answer 1

Correct Answer - Option 2 : x(t-y)ty^-1

Given:

Time taken to complete the journey = t hours

Time taken to complete the journey after increasing speed = (t - y) hours

Formula used:

Distance = Speed × Time

Calculation:

Let the distance be D and the initial speed of the car be a kmph.

According to the first condition,

D = at      ----(1)

According to the second condition,

D = (a + x)(t - y)      ----(2)

From equation (1) and equation (2),

at = (a + x)(t - y)

⇒ at = at + xt - ay - xy

⇒ ay = x(t - y)

⇒ a = x(t - y)/y

Put the value of a in equation 1,

D = x(t - y)ty^-1

∴ The distance is x(t - y)ty^-1 km.