Answer:
3.333 hours
Step-by-step explanation:
First, you need the distance that Ben ([tex]D_{B1}[/tex]) and Sam ([tex]D_{S1}[/tex]) have traveled in 40 minutes (Multiply the time by the speed):
[tex]t=40 min( \frac{1 hour}{60 min})=2/3 hours\\D_{B1}=2/3(15)=10 miles\\D_{S1}=2/3(12)=8 miles[/tex]
While Ben is fixing the flat tire Sam keeps going, the distance traveled by Sam ([tex]D_{S2}[/tex] in one hour is:
[tex]D_{S2}=1(12)=12 miles[/tex]
At this moment the distance traveled by Ben is in total 10 miles, the total distance traveled by Sam is 20 miles, and the distance between them is 10 miles. Let [tex]x[/tex] be the distance from the position when Ben fixed its tire to the position when he catches up with Sam, and [tex]t[/tex] the time
[tex]x=15t[/tex]
The distance traveled by Sam at the same time t is [tex]x-10[/tex].
[tex]x-10=12t\\x=12t+10[/tex]
Substitute this equation in the other and solve for [tex]t[/tex]:
[tex]12t+10=15t\\10=15t-12t\\10=3t\\t=10/3\approx3.333hours[/tex]
