Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's average speed/

Jose's speed = X mi/h.

Kayia's speed = (X+35)mi/h.
They had traveled the same distance:
Dj = Dk.
D=Xmi/h * (2.1+1.2)h=(X+35)mi/h * 1.2h.
3.3x = 1.2x + 42
2.1x = 42
X = 2o mi/h.

To find Jose's average speed, we need to determine the distance he traveled.

Let's break down the information given:
- Jose left the airport and traveled toward the mountains.
- Kayla left 2.1 hours later.
- Kayla was traveling 35mph faster than Jose.
- After 1.2 hours, Kayla finally caught up.

Since Jose left the airport earlier than Kayla, he had a head start of 2.1 hours. This means that Jose had been traveling for 2.1 hours before Kayla even started.

Let's calculate the distance Kayla traveled during the 1.2 hours to catch up to Jose:
Distance = Speed × Time
Distance = (J + 35) × 1.2 [Where J is Jose's speed in mph]

Now, let's calculate the distance Jose traveled in total:
Distance = Speed × Time
Distance = J × (1.2 + 2.1)

Since Kayla traveled the same distance as Jose during her 1.2-hour period, we can equate the distances:
(J + 35) × 1.2 = J × (1.2 + 2.1)

Simplifying this equation, we get:
1.2J + 42 = 3.3J

Now, we can solve for J (Jose's speed):
42 = 3.3J - 1.2J
42 = 2.1J
J = 42 / 2.1
J = 20

Therefore, Jose's average speed is 20 mph.