Question

Tevin left his house and rode his bike into town at 6 mph. Along the way he got a flat so he had to turn around and walk his bike back to his house traveling 3 mph. If the trip down and back took 12 hours, how far did he get before his tire went flat?

Answer 1

Answer:

Distance covered by Tevin before his tire went flat = 24 miles

Explanation:

Let x be the distance covered by Tevin before his tire went flat.

Given:

Tevin drives his bike in the town = 6 mph  

Tevin back to his house = 3 mph

Total taken time by Tevin = 12 hours

We need to find the distance covered by Tevin in 12 hours.

Solution:

Using speed formula    

$Speed =\frac{Distance}{Time}$

We write the above formula for Time.

$Time=\frac{Distance}{Speed}$-----------(1)

Time taken by Tevin when biking in town

Substitute speed = 6 mph and distance = x in equation 1.

$Time=\frac{x}{6}$  ----------(2)

Time taken by Tevin when he is back to his house.

Substitute speed = 3 mph and distance = x in equation 1.

$Time=\frac{x}{3}$   -------------(3)

Total time taken by Tevin.

Total taken time by Tevin = Time taken when biking in town + Time taken when Tevin back to his house.

Substitute time value from equation 2 and 3 in above equation and total time = 12 hours.

$12=\frac{x}{6}+\frac{x}{3}$

Now, we solve the above equation for x.

$12=\frac{x+2x}{6}$

$12\times 6=x+2x$

$72=3x$

$x=\frac{72}{3}$

$x=24\ mi$

Therefore, distance covered by Tevin in 12 hours is equal to 24 miles.