Question

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Answer 1

Step 1: Given data

Let the speed of the first car at A be x kmph and the speed of the car at B be y kmph

When the cars travel in the same direction Relative Speed is S=x−y

Distance D=100 km

Time, t=5 hours

Step 2: Formula used

Since, $Speed\left(S\right)=\frac{Dis\tan ce\left(D\right)}{Time\left(T\right)}$

Therefore, Distance $\left(D\right)=S\times T$

Step 3: Calculating the speed of the car

Substitute the given values in $\left(D\right)=S\times T$

we get

⇒$100=\left(x-y\right)\times 5$

∴x−y=20.......(i)

When cars travel in opposite directions, the relative Speed is x+y

Distance=100 km

Time (T)=1 hours

Distance $D=S\times T$

⇒100=(x+y)

x+y=100.......(ii)

Adding equations (i) & (ii), we get

x−y+x+y=20+100

⇒2x=120

∴$x=60km{h}^{-1}$

From equation(i), y=60−20

∴ $y=40km{h}^{-1}$

Hence, the speed of the car at $A=60km{h}^{-1}$ and

Speed of the car at $B=40km{h}^{-1}$