Question

a bus leaves manila for Bulacan at noon 50.0 km away at a constant speed covering 25.0 km in 1.25 hours. however when it was 25. km away from Manila, it had a flat tire. it takes 30 minutes to have4 the tire replaced. afterwards, the bus travels at the same rate for the rest of the trip. suppose a second bus leaves Bulacan at noon for manila at 15 km/hr, will the two buses meet? if yes, when and where will they meet? Draw the displacement versus time graph for each buses.

Answer 1

give t is time in minutes, and x is distance from start in km
for bus1:
\[0 \le t \lt 30 : x _{1} = 50 . t / 60\]
\[30 \le t \lt 60 : x_{1} = 25 \]
\[60 \le t \lt 75 : x_{1} = 25 + 50 . (t-60)/60 \]
for bus2:
\[ 0 \le t : x_{2} = 15 . t / 60 \]
if they would ever meet, it must be before t = 60, however at t=60:
\[ x_{1} = 25 \]
\[ x_{2} = 15 \]
so they never meet.