Question

Two railway stations, X and Y, are 140 miles apart in a straight line. One train starts from X at 8 a.m. and travels towards Y at 30 miles per hour. Another train starts from Y at 9 a.m. and travels towards X at a speed of 35 miles per hour. At what time will they meet?

• A. 11 a.m.
• B. 1 a.m.
• C. 3 p.m.
• D. 12 p.m.

Answer 1

The correct option is A 11 a.m.

Let assume they meet at 'a' hours after 8 a.m.

Speed of train X = 30 miles per hour

Distance = Speed $\times$ Time

Distance covered by train X in 'a' hours = 30a miles

Train Y starts at 9 a.m., which is one hour after train X starts. This means that the time taken is 1 hour less as compared to train X.

Distance covered by train Y in 'a – 1' hours = 30(a – 1) miles

$\therefore$ 30a + 35(a – 1) = 160

$⟹$ 30a + 35a – 35 = 160

$⟹$ 65a – 35 = 160

$⟹$ 65a = 160 + 35

$⟹$ 65a = 195

$⟹$ a = $\frac{195}{65}$

$⟹$ a = $3$

Therefore, they meet at 3 hours after starting at 8 a.m. So, they meet at 11 a.m.