Average Speed: Using variables

The owner of a pizzeria suspects that one of his delivery drivers has taken too long of a break.

He knows that the driver traveled for 45 minutes at a speed of 90 km/h and then quickly returned the same way at a speed of 67.5 km/h.

In the middle, he took a break. The manager also knows that the driver's average speed throughout the day is 54 km/h.

How long was the break?

45 minutes

Ricardo travels 18 km at a speed of X km/h and then doubles his speed.

Then he covers another 12 km, rests for half an hour, and then continues at his initial speed for another 10 km.

What is his average speed?

$\frac{80x}{68+x}$ km/h

A jaguar begins to stalk a deer at 6 in the morning.

After X minutes, it begins to chase the deer at a speed of 70 km/h for 8 minutes.

After that, the deer and jaguar both begin to accelerate and run for another 4 minutes until the deer is caught.

The average speed of the jaguar from the start of the ambush to the catching the deer is 80 km/h.

Express the speed of the jaguar in the last 4 minutes in terms of x.

$100+20x$ km/h

Gabriela runs 4km at a speed of 8km/h, then another 6 km.

Her average speed is $5x$ km/h.

Express her speed during the last 6 km in terms of X.

$\frac{12x}{4-x}$ km/h

A turtle starts its journey towards the sea 38 meters away from it.

In the first 20 meters, its speed is X km/h. It rests for 20 minutes and then continues its journey at a speed $1\frac{1}{4}$ times greater than its previous speed.

What is the average speed?

$\frac{142.5x}{129+1250x}$ km/h