Solve for Average Speed: Jogging and Driving Distance Calculation

[jwang023]

Homework Statement

You jog at 9.5 km/hr for 8.0 km. You jump into a car and drive 16 km. What speed of the car do you need to cover a total distance of 24 km with an average speed of 22 km/hr

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Average speed = Total distance/Total time.
In the problem total distance and average speed. Find the total time.
Find the jogging time. From that find the driving time.
Driving distance is given. You can find the driving time. From that find the velocity of the car.

 

[kerimek]

To solve for average speed, we can use the formula: average speed = total distance / total time.

To find the total time, we need to add the time it takes to jog 8.0 km at 9.5 km/hr to the time it takes to drive 16 km at the unknown speed.

Time for jogging = 8.0 km / 9.5 km/hr = 0.84 hours

Time for driving = 16 km / x km/hr

Total time = 0.84 hours + 16 km / x km/hr

To find the average speed of 22 km/hr, we can set up the equation:

22 km/hr = (8.0 km + 16 km) / (0.84 hours + 16 km / x km/hr)

Simplifying, we get:

22 km/hr = 24 km / (0.84 hours + 16 km / x km/hr)

Multiplying both sides by the denominator, we get:

22 km/hr * (0.84 hours + 16 km / x km/hr) = 24 km

Solving for x, we get:

x = 12.75 km/hr

Therefore, to cover a total distance of 24 km with an average speed of 22 km/hr, the car needs to travel at a speed of 12.75 km/hr.