Question

John covered a part of his journey at $20\text{kmph}$, and the remaining part at $70\text{kmph}$. He took a total of $8\text{hr}$ to cover a distance of $400\text{km}$. For how much time did he travel at $20\text{kmph}$?

• A. $4\text{hr}$ and $12\text{min}$
• B. $3\text{hr}$ and $20\text{min}$
• C. $4\text{hr}$ and $40\text{min}$
• D. $3\text{hr}$ and $12\text{min}$

Answer 1

The correct option is D $3\text{hr}$ and $12\text{min}$

Let the total time that John has travelled at the speed of $20\text{kmph}$ be $T$.

Distance is the product of speed and time. Hence, the distance covered at a speed of $20\text{kmph}$ is:
$s_1=20\times T.........\left(i\right)$

The total time taken covered is $8\text{hr}$. Thus, the time to cover the remaining distance is:
$t_2=8-T$

The remaining distance which is covered at a speed of $70\text{kmph}$ is:
$s_2=70\times (8-T).......\left(ii\right)$

Given, the total distance covered:
$s=400km.......\left(iii\right)$
But,
$s=s_1+s_2$
From (i), (ii) and (iii), we get
$400=20\times T+70\times (8-T)$
$50\times T=160$
$T=3.2\text{hr}$
We know $1\text{hr}=60\text{min}$
$⟹0.2\text{hr}=0.2\times 60=12\text{min}$
$\therefore T=3\text{hr}$ and $12\text{min}$