Word equation:Two buses were coming from two different places situated just in the opposite direction. The average speed of one bus is 5 km/hr more than that of another one and they had started...
Two buses were coming from two different places situated just in the opposite direction. The average speed of one bus is 5 km/hr more than that of another one and they had started their journey in the same time. If the distance between the places is 500 km and they meet after 4 hours, find their speed.
given : the distance between the two places from where the buses start = 500 km, The time after whuch they meet each other = 4hr. and the Avg. speed of one bus is 5 km/hr more Than the other bus.
Let the bus A start from a place P and the bus B start from the place Q and let they meet at a point R after the journey of 4hr. the distane PQ = 500 km.
Let the avg. speed of the bus A = x km/hr the the avg. speed of the second bus B= (x + 5)km/hr.
The distance travelled by the bus A in 4hr. = PR = 4x The distance travelled by the bus B in 4hr. = QR = 4(x + 5)
PR + QR = PQ
4x + 4(x + 5) = 500
Or, 4x + 4x + 20 = 500
Or, 8x = 500 - 20
Or, 8x = 480
Or, x = 480/8 = 60
Therefore x = 60 km/hr and x + 5 = 60 + 5 = 65
Hence The average speed ot the two buser are : 60km/hr and 65km/hr
To start, you have represent the rate of each bus.
Let x = rate of the first bus and x + 5 = rate of the 2nd bus.
Note that distance = rate*time and t = 4. The distance they traveled in 4 hours was equal to 500. So the working equation should be:
x*4 + (x + 5)*4 = 500
4x + 4x + 20 = 500
8x + 20 = 500 subtracting 20 from both sides
8x = 480 divide both sides by 8
x = 60 kph
x + 5 = 65 kph
The speed of the buses are 60 kph and 65 kph.