Two jets are traveling toward each other and are 4000km apart. The rate of one jet is 100km/h faster than the rate of the other. If the jets pass each other after 2.5 hours, what is the rate of the faster jet?

rate of slower jet ---- x km/h

rate of faster jet ----- x+100 km/h

solve for x

2.5x+ 2.5(x+100) = 4000

(I got x = 750 , so the faster jet goes 850 km/h)

Let's assume the rate of the slower jet is x km/h.

Since the rate of the faster jet is 100 km/h faster than the rate of the slower jet, the rate of the faster jet is (x + 100) km/h.

When the two jets are traveling toward each other, their combined rate is the sum of their individual rates.

So, the combined rate of the two jets is x km/h + (x + 100) km/h = 2x + 100 km/h.

We know that the jets pass each other after 2.5 hours, and the distance between them is 4000 km.

Distance = Rate × Time

Therefore, 4000 km = (2x + 100 km/h) × 2.5 h.

Let's solve for x:

4000 km = 5x + 250 km

3750 km = 5x

x = 3750 km / 5

x = 750 km/h

So, the rate of the slower jet is 750 km/h.

The rate of the faster jet is x + 100 km/h = 750 km/h + 100 km/h = 850 km/h.

Therefore, the rate of the faster jet is 850 km/h.

To find the rate of the faster jet, we can set up a system of equations based on the information given.

Let's call the rate of the slower jet "x" km/h.

Since the rate of the faster jet is 100 km/h faster than the rate of the slower jet, we can say that the rate of the faster jet is (x + 100) km/h.

When the two jets are traveling toward each other, their rates add up. So, the combined rate of both jets is (x + x + 100) km/h.

We know that distance equals rate multiplied by time. In this case, the total distance between the jets is 4000km, and they pass each other after 2.5 hours.

So, we can set up the following equation:

4000 = (x + x + 100) * 2.5

To solve this equation, we will simplify it:

4000 = (2x + 100) * 2.5

Now, we can distribute the 2.5 to simplify further:

4000 = 5x + 250

Next, let's isolate the variable x by subtracting 250 from both sides:

4000 - 250 = 5x

3750 = 5x

To solve for x, we divide both sides of the equation by 5:

x = 3750 / 5

x = 750

So, the rate of the slower jet is 750 km/h.

Finally, to find the rate of the faster jet, we add 100 to the rate of the slower jet:

Rate of the faster jet = 750 + 100 = 850 km/h

Therefore, the rate of the faster jet is 850 km/h.