1. The distance between towns A and B is 360km. A minibus left A at 8.15am and traveled towards B atan average speed of 90km/hr. A matatu left B two and a third hours later on the same day andtraveled towards A at an average speed of 110km/hr.a) i) At what time did the two vehicles meet? (4mrks)ii) How far from A did the vehicles meet?(2mrks)b) A motorist started from his home at 10.30am on the same day and travelled at an averagespeed of 100km/hr. He arrived at B at the same time as the minibus. Calculate the distance fromA to his house.(4 mks)
Answers
Step-by-step explanation:
(i)before matatu started its journey the bus had covered 90 km.
so the remaining distance is 90 km.
the avr. speed of minibus and matatu are 90km/hr and 110km/hr respectively.
and as they are in the opposite directions their speeds can be added to get the total speed.
so, the total speed is 200km/hr
time taken will be 90/200 hr
=9/20*60 min
=27 min
they will meet 27 min after matatu started.
(ii)as they met after 27min or 9/20 hr after matatu started its journey.
so it might have covered distance that is= 110*9/20
= 49.5km
so distance between meeting point and A is 360-49.5 km
=310.5 km
(iii) according to the question the bus would have taken 4 hr to reach b i.e. at 12:15
and the motorcyclist took only 1 hr 45 min to reach Bat an avr. speed of 100km/hr.
time taken=1hr 45min=1 whole 3/4 hr=7/4 hr
speed = 100 km/hr
distance travelled = 7/4*100
= 25*7
= 175 km
so distance between his home and A is 360-175 km
=185 km