Question

A car travels from A to B at 60 km/h and returns at 40 km/h. If the total time taken is 5 hours, what is the distance between A and B?

• A. 100 km
• B. 120 km
• C. 150 km
• D. 180 km

Hint:

For round-trip problems, use the total time equation and simplify with the LCM of the denominators.

Answer 1

The Correct Option is B

- Step 1: Let the distance be $D$ km. Time from A to B = $\dfrac{D}{60}$ hours; return = $\dfrac{D}{40}$ hours.
- Step 2: Total time = $\dfrac{D}{60} + \dfrac{D}{40} = 5$.
- Step 3: LCM of 60 and 40 is 120. Equation: $\dfrac{D}{60} + \dfrac{D}{40} = \dfrac{2D + 3D}{120} = \dfrac{5D}{120} = 5$.
- Step 4: Solve: $\dfrac{5D}{120} = 5$, so $D = 120$.
- Step 5: Verify: Time A to B = $\dfrac{120}{60} = 2$ hours; return = $\dfrac{120}{40} = 3$ hours. Total = $2 + 3 = 5$ hours.
- Step 6: Check options: Option (b) is 120 km, which matches.