Question

Two cars start at the same time from towns A and B, and travel with constant but different speeds towards each other. They pass each other at 70 km from town A, and continue to the opposite town, where they turn around without stopping. The cars pass each other again 40 km from town B. The distance between the two towns is

• A. 165
• B. 170
• C. 175
• D. 180

Answer 1

The correct option is B

170

Method 1:
Assume that the distance between the towns is x km. The first time the cars pass each other, the first car (from town A) has gone 70 km and the other has gone
(x-70)km. These distance were covered in the same time, so the ratio of the speeds of the cars is $\frac{70}{x-70}.$
The next time they meet, the first car has travelled (x+40) km and the second car has travelled (2x-40) km.Thus the ratio of the speeds is also equal to $\frac{(x+40)}{2x-40}.$ We can equate the two ratios to get $\frac{70}{x-70}=\frac{(x+40)}{2x-40}$ , so 70(2x-40)=(x+40)(x-70). This gives $140x-2800=x^2-30x-2800$, so, x(x-170) =0. The towns are 170 km apart.

Method 2: Reverse Gear:
Go from answer options,
Since the time is constant in both cases, the distance ratios should also remain the same. Assuming that option (b) is correct

$\frac{70}{100}=\frac{210}{300}$

Hence,Distance Ratio 1 (first Meeting =Distance Ratio(Second Meeting) Our Assumption is correct. Answer os option (b)).