Question

Peter can cover a certain distance in 1 hour 24 minutes by covering two-thirds of the distance at 4 kmph and the rest at 5 kmph. The total distance is :

• A. 5.5 km
• B. 6.5 km
• C. 5 km
• D. 6 km

Hint:

Break down the journey into parts where the speed is constant. Use the formula Time = Distance / Speed for each part and sum the times to equal the total time given.

Answer 1

The Correct Option is D

Step 1: Convert the total time to hours.
Total time = 1 hour 24 minutes = 1 hour + \( \frac{24}{60} \) hours = 1 hour + 0.4 hours = 1.4 hours. Step 2: Let the total distance be \(D\) km.
Distance covered at 4 kmph = \( \frac{2}{3} D \) km.
Distance covered at 5 kmph = \( D - \frac{2}{3} D = \frac{1}{3} D \) km.
Step 3: Calculate the time taken for each part of the journey.
Time taken for the first part = \( \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{2}{3} D}{4} = \frac{2D}{12} = \frac{D}{6} \) hours.
Time taken for the second part = \( \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{1}{3} D}{5} = \frac{D}{15} \) hours.
Step 4: Set up an equation for the total time.
Total time = Time for the first part + Time for the second part $$1.4 = \frac{D}{6} + \frac{D}{15}$$ Step 5: Solve the equation for \(D\).
Find a common denominator for 6 and 15, which is 30.
$$1.4 = \frac{5D}{30} + \frac{2D}{30}$$
$$1.4 = \frac{5D + 2D}{30}$$
$$1.4 = \frac{7D}{30}$$
Multiply both sides by 30:
$$1.4 \times 30 = 7D$$
$$42 = 7D$$
$$D = \frac{42}{7} = 6$$
The total distance is 6 km.