Question 267665
Lucas is 1/3 mile away from home bicycling at 20 miles per hour when his brother takes off on his bike to catch up.
 How fast must Lucas's brother go to catch him a mile from home.
:
Briefly, bro has to travel 1 mi in the same time that L travels 2/3 of a mile
:
Let s = bro's speed to accomplish difficult feat
:
Write a time equation: Time = dist/speed
:
bro's time = L's time
{{{1/s}}} = {{{(2/3)/20}}}
:
{{{1/s}}} = {{{2/60}}}
:
{{{1/s}}} = {{{1/30}}}
Cross multiply
s = 30 mph bro has pedal to catch L 1 mi from home
;
:
Check this by finding the times
1/30 = .033 hrs
.667/20 = .033 hrs (about 2 min)