You and your roommate are moving to a city 340 mi away. Your roommate drives a rental truck at a constant 60 mi/h, and you drive your car at 70 mi/h. The two of you begin the trip at the same instant. An hour after leaving, you decide to take a short break at a rest stop. If you are planning to arrive at your destination a half hour before your roommate gets there, how long can you stay at the rest stop before resuming your drive?

T_stop = 0.30952 hr = 18.57 mins

Explanation:

Given:

- The distance between two towns S = 340 mi

- Speed of the room-mate v_r = 60 mi/h

- Our Speed v_o = 70 mi / h

- Both drive at their receptive speeds for 1 hr.

- We stop for time t_stop

- We need to arrive 0.5 hrs earlier than our room mate

Find:

how long can you stay at the rest stop before resuming your drive?

Solution:

- Total time taken by room-mate:

T_r = S / v_r

T_r = 340 / 60 = 17/3 hrs

- Total time taken by you:

T_o = T_1hr + T_stop + T_resume

- We are given that we must reach 0.5 hrs earlier than your room-mate:

T_o = T_r - 0.5

- Hence,

T_stop = T_r - 0.5 - T_resume - T_1hr.

- Plug in the values:

T_stop = 17/3 - 0.5 - 1 - (340 - v_o*1hr) / v_o

T_stop = 31/6 - 1 - (340 - 70) / 70

T_stop = 25/6 - 27/7

T_stop = 0.30952 hr = 18.57 mins