Question

On a long-distance biking trip, Annike started biking at 7 a.m., and her average speed was 11 miles per hour. Celia started at 8 a.m., and her average speed was 14 miles per hour. At what time will the two bikers have completed the same number of miles?At what time will the two bikers have completed the same number of miles

Answer 1

Let´s remember that the formula to the position of a particula that moves in a line with constant speed is:

`x=x_0+vt_{}`

so, lets apply this formula for Annike, and for Celia:

First, for annika

`x_A=0+11t=11t`

Then, for celia:

`x_C=14(t-1)`

Then, to know At what time will the two bikers have completed the same number of miles we need to equalize the two formulas of the position and solve for t:

`11t=14(t-1)\Leftrightarrow11t-14t=-14\Leftrightarrow3t=14\Leftrightarrow t=(14)/(3)\approx4.67`

so the answer is that they complete the same number of miles after 4.67 hours