Question

An aeroplane takes off 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/h from its usual speed. Find its usual speed.

• A. 1000 km/h
• B. 750 km/h
• C. 850 km/h
• D. 650 km/h

Answer 1

The Correct Option is B

To solve this problem, let's first establish the relationship between speed, distance, and time using the formula:
Distance = Speed × Time

We know:

• Distance = 1500 km
• Scheduled Time = Usual Time (T)
• Delayed Time = Usual Time - 0.5 hours (due to 30 minutes delay)
• Increased Speed = Usual Speed + 250 km/h

Now, apply the distance formula for both scenarios:

• Usual journey: 1500 = Usual Speed × T
• Delayed journey: 1500 = (Usual Speed + 250) × (T - 0.5)

From the usual journey equation, solve for T:

T = 1500 / Usual Speed

Substitute T into the delayed journey equation:

1500 = (Usual Speed + 250) × (1500 / Usual Speed - 0.5)

Simplify the expression:

1500 = (Usual Speed + 250) × (1500 - 0.5 × Usual Speed) / Usual Speed

Expand and simplify:

1500 = [1500 × Usual Speed + 375000 - 0.5 × Usual Speed² - 125] / Usual Speed

Multiply through by Usual Speed to clear the denominator:

1500 × Usual Speed = 1500 × Usual Speed + 375000 - 0.5 × Usual Speed² - 125

Cancel 1500 × Usual Speed on both sides:

0 = 375000 - 0.5 × Usual Speed² - 125

0.5 × Usual Speed² = 374875

Usual Speed² = 749750

Solve for Usual Speed by taking square root:

Usual Speed ≈ √749750 ≈ 750 km/h

Therefore, the usual speed of the airplane is 750 km/h.