Question

X and Y are two cities 450km apart. Two cars start at the same time from X and Y at 9 a.m. The car from X travels at the rate of 50km/h and the car from Y travels at the rate of 40km/h. When and at what distance from X will they meet

Answer 1

Answer :

Given : Distance between X and Y = 450 km ,

Two cars start at the same time from X and Y at 9 a.m. ,

The car from X travels at the speed of 50 km/hr.

And

The car from Y travels at the speed of 40 km/hr.

Let , The car from X travels at the speed of 50 km/hr cover total distance at the point of meet = x km

Then ,

The car from Y travels at the speed of 40 km/hr cover total distance at the point of meet = 450 - x km

And to reach at same point they must have taken same time .

We know : Time = $\frac{\mathrm{Distance}}{\mathrm{Time}}$ , So

$$\begin{gathered} \frac{x}{50}=\frac{450-x}{40} \\ \Rightarrow 40x=50\left(450-x\right) \\ \Rightarrow 40x=22500-50x \\ \Rightarrow 90x=22500 \\ \Rightarrow x=\frac{22500}{90} \\ \mathbf{\Rightarrow }\mathbf{}\mathit{x}\mathbf{}\mathbf{}\mathbf{=}\mathbf{250} \end{gathered}$$

So, They meet 250 km away from X .

And time taken by that car = $\frac{250}{50}$ = 5 hr

So, time 9 : 00 + 5 hr = at 2 : 00 PM ( Ans )