Answer to Question #103361 in Algebra for Zawadi

Question

A cyclist Leaves town A for town B at 11:30 am and travels at an average speed of 15km/hr.30 minutes later a bus leaves town A from town B arriving at 12:30pm. Town A is 30km to town B.Determine the average speed of the bus? Determine the distance from town A where the cyclist met the bus? The time they met? Find the time the cyclist arrived in town B

Answer 1

$S_{AB}=30 km, V_c=15 km/h$

the cyclist time from A to B:

$t_c=S_{AB}/V_c=2 h$

the bus starts to move after 30 minutes, during which time the cyclist will travel the distance:

$S_{AC}=V_c \cdot 0.5h=7.5km$

the bus moved from 12:00 to 12:30 (30 minutes) from B to A (30 km), then the average speed of the bus:

$V_b=S_{AB}/0.5h=60 km/h$

the bus and the cyclist met through:

$t_x=S_{CB}/(V_c+V_b)=\frac{30km-7.5km}{15km/h+60km/h}=0.3h$

during this time the cyclist will pass:

$S_{CD}=V_c \cdot 0.3h=4.5km$

meeting at a distance from A:

$S_{AD}=S_{AC}+S_{CD}=12km$

meeting time:

$t=11:30+30min+0.3h=12:18pm$

the time the cyclist arrived in town B:

$11:30+t_c=13:30pm$

Answer:

the average speed of the bus: 60 km/h

the distance from town A where the cyclist met the bus: 12 km

the time they met: 12:18 pm

the time the cyclist arrived in town B: 13:30 pm