Question

A man travels 300 km, partly at 60 km/h and partly at 80 km/h. If the total time taken is 4.5 hours, how many kilometers did he travel at 60 km/h?

• A. 120 km
• B. 150 km
• C. 180 km
• D. 200 km

Hint:

For time and distance problems with two speeds, set up the equation using total time and solve using the LCM to clear denominators.

Answer 1

The Correct Option is C

- Step 1: Let the distance traveled at 60 km/h be $x$ km. Then, distance at 80 km/h is $300 - x$ km.
- Step 2: Time taken at 60 km/h = $\dfrac{x}{60}$ hours; at 80 km/h = $\dfrac{300 - x}{80}$ hours.
- Step 3: Total time is 4.5 hours, so $\dfrac{x}{60} + \dfrac{300 - x}{80} = 4.5$.
- Step 4: Multiply through by 240 (LCM of 60 and 80): $4x + 3(300 - x) = 1080$.
- Step 5: Simplify: $4x + 900 - 3x = 1080$, so $x = 1080 - 900 = 180$.
- Step 6: Verify: Time at 60 km/h = $\dfrac{180}{60} = 3$ hours;
at 80 km/h = $\dfrac{120}{80} = 1.5$ hours.
Total = $3 + 1.5 = 4.5$ hours. Option (c) matches.