Question

While boarding a plane, a passenger got hurt. The pilot, showing promptness and concern, made arrangements to hospitalize the injured, and so the plane started late by 30 minutes. To reach the destination, 1500km away in time, the pilot increased the speed by 100km/hr. Find the original speed of the plane.

Answer 1

To calculate the original speed of the plane, we set up an equation based on the fact that the plane traveled 1500km and was delayed by 30 minutes, but it increased speed by 100km/hr to reach on time. We solve the equation deriving from the change in speed and delay to find the original speed.

Step-by-step explanation:

The question asks us to find the original speed of a plane which had to increase its speed after a delay in order to reach its destination on time. The key to solving this problem is to use the relationships between speed, distance, and time. We are given that the plane's increased speed is by 100 km/h to cover a distance of 1500km.

Let the original speed be x km/h. The time taken by the plane at the original speed to travel 1500km would be 1500/x hours. Now, because of the 30-minute delay, the plane must travel at the speed of (x + 100) km/h to reach on time. The time taken to travel the same distance at this new speed is 1500/(x + 100) hours.

Since the plane is delayed by 30 minutes, or 0.5 hours, the equation to represent the time to reach on time would be:

1500/x - 1500/(x + 100) = 0.5

Now we have an equation with one variable, which we can solve to find the value of x. Multiplying both sides by x(x + 100) to get rid of the denominators gives:

1500(x + 100) - 1500x = 0.5x(x + 100)

Simplifying this equation will give us the original speed of the plane.