Question

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less,it would have needed 6 hours more. The distance, in km, travelled by the train is

• A. 800
• B. 640
• C. 720
• D. 780

Answer 1

The Correct Option is C

Let the distance traveled by the train be $d$ km, and the original speed be $s$ km/hr. We are given two conditions:
If the speed is increased by 6 km/hr, the time taken is reduced by 4 hours.
If the speed is decreased by 6 km/hr, the time taken is increased by 6 hours.
Using the formula for time $\text{time} = \frac{\text{distance}}{\text{speed}}$, we write the time for the three conditions:
Original time: $\frac{d}{s}$
Time with increased speed: $\frac{d}{s+6}$
Time with decreased speed: $\frac{d}{s-6}$
From the problem, we know:
\[ \frac{d}{s} - \frac{d}{s+6} = 4 \quad \text{and} \quad \frac{d}{s-6} - \frac{d}{s} = 6 \]
Solving this system of equations, we first multiply both sides of each equation by the denominators to eliminate fractions and solve for $d$.
After solving, we find that $d = 720$.
Thus, the distance traveled by the train is 720 km.