Two planes leave Manila for a southern city, a distance of 900 km. Plane A travels at a ground speed of 90 kph faster than the plane B. Plane A arrives in their destination 2 hours and 15 minutes ahead of Plane B. What is the ground speed of plane A?

Sure, let's solve this step by step.

Step 1: Convert the time difference to hours 2 hours and 15 minutes is equal to 2.25 hours.

Step 2: Set up the equation We know that speed = distance/time. We can set up the following equations based on the information given:

For Plane B: Speed = 900 km / (time in hours)

For Plane A: Speed = 900 km / (time in hours - 2.25)

We also know that the speed of Plane A is 90 kph faster than Plane B. So we can set up the following equation:

900 / (time - 2.25) = 900 / time + 90

Step 3: Solve the equation To solve for time, we can first simplify the equation by multiplying all terms by time*(time - 2.25) to get rid of the denominators:

900time = 900(time - 2.25) + 90time(time - 2.25)

This simplifies to:

900time = 900time - 2025 + 90time^2 - 202.5time

Rearranging terms gives us a quadratic equation:

90time^2 - 202.5time - 2025 = 0

Dividing all terms by 90 to simplify gives:

time^2 - 2.25*time - 22.5 = 0

Solving this quadratic equation gives us time = 6 hours or time = -3.75 hours. We discard the negative solution as time cannot be negative.

Step 4: Substitute the time into the speed equation Substituting time = 6 hours into the speed equation for Plane A gives:

Speed = 900 km / (6 hours - 2.25 hours) = 900 km / 3.75 hours = 240 kph

So, the ground speed of Plane A is 240 kph.