Question

Aa plane left 30 minutes late than its scheduled time and in orser to rache the destination 1500km away in time it had to increase its speed by 100km/hr from the ususal speed.find usual speed

Answer 1

Solution :-

Let the original speed of train be x km/hr

New speed = (x + 100) km/hr

We know that,

Time = Distance / Speed

Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.

According to the question,

=> 1500/x - 1500/(x + 100) = 1/2

=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2

=> 2(15000) = x(x + 100)

=> 30000 = x² + 100x

=> x² + 100x - 30000 = 0

=> x² + 600x - 500x - 30000 = 0

=> x(x + 600) - 500(x + 600) = 0

=> (x - 500) (x + 600) = 0

=> x = 500 or x = - 600

∴ x ≠ - 600 (Because speed can't be negative)

Hence,

Its usual speed = 500 km/hr

Answer 2

Explanation:

Solution :-

Let the original speed of train be x km/hr

New speed = (x + 100) km/hr

We know that,

Time = Distance / Speed

Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.

According to the question,

➡️ 1500/x - 1500/(x + 100) = 1/2

➡️ (1500x + 15000 - 1500x)/x(x + 100) = 1/2

➡️2(15000) = x(x + 100)

➡️30000 = x² + 100x

➡️ x² + 100x - 30000 = 0

➡️x² + 600x - 500x - 30000 = 0

➡️x(x + 600) - 500(x + 600) = 0

➡️ (x - 500) (x + 600) = 0

➡️x = 500 or x = - 600

∴ x ≠ - 600 (Because speed can't be negative)

Hence,

Its usual speed = 500 km/hr

hope this helps you ☺️