Question

Ramesh travels $760km$ to his home partly by train and partly by car. He takes $8hr$, if he travels $160km$ by train and the rest by car. He takes $12$ minutes more, if he travels $240km$ by train and the rest by car. Find the speed of train and the car.

• A. Speed of train $=80km/hr$ and speed of car $=100km/hr$
• B. Speed of train $=40km/hr$ and speed of car $=50km/hr$
• C. Speed of train $=60km/hr$ and speed of car $=120km/hr$
• D. Speed of train $=70km/hr$ and speed of car $=130km/hr$

Answer 1

The correct option is A Speed of train $=80km/hr$ and speed of car $=100km/hr$

Let the speed of train be xkm/hr

and the speed car be ykm/hr respectively.

We know that $Speed=\frac{Distance}{Time}\Rightarrow Time=\frac{Distance}{Speed}$

In Case 1

Distance travelled by train $=$ 160km

Distance travelled by car $=$ (760-160)km $=$ 600km

Time taken by train+Time taken by car $=$ 8 hours

Hence the equation becomes

$\frac{160}{x}+\frac{600}{y}=8$

In case 2

Distance travelled by train $=$ 240km

Distance travelled by car $=$ (760-240)km = 520km

Time taken by train+Time taken by car $=$ 8 hours+12 minutes

Hence the equation becomes

$\frac{240}{x}+\frac{520}{y}=\frac{41}{5}......\left(2\right)$

Hence we get two equations

$\frac{160}{x}+\frac{600}{y}=\mathrm{8.........}\left(1\right)\frac{240}{x}+\frac{520}{y}=\frac{41}{5}......\left(2\right)$

$Let\frac{1}{x}=pand\frac{1}{y}=q$

Hence we get equations

160p + 600q $=$ 8........(3)

240p + 520q $=$ 41/5...(4)

Solving equations (3) and (4)we get p$=$1/80 and q $=$1/100

$Hencep=\frac{1}{x}\Rightarrow x=\frac{1}{p}=80Similaryy=\frac{1}{q}=100$

Solving we get x $=$ 80 and y $=$ 100

hence, speed of train =80km/hr and speed of car =100km/hr.