Question

Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

A. 2 hours
B. 4 ½ hours
C. 5 ¾ hours
D. 6 hours
E. 7 ½ hours

Answer is B. How so?

Answer 1

For some reason I got 2 hours

Answer 2

First, they meet after both have biked the same distance.
the first goes a distance of (rate * time= distance) 6*T
the second travels 10*(T-3) (starts 3 hours later, so he bikes less time

set the distances equal
6T= 10(T-3)
solve for T

Answer 3

T is the time of the first biker
Question asks for the time for the 2nd biker which is T-3

Answer 4

We could have set it up as T = time of the second biker. This means the 1st biker goes for T+3 hours
and
6(T+3)= 10T
now T is the time the 2nd biker has gone before they meet.

Answer 5

Maybe the hardest part is realizing
they meet after both have biked the same distance.

then you need to know rate*time= distance

then how to translate the info into an equation.
then how to solve the equation