# 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...

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 their journey in the same time. If the distance between the places is 500 km and they meet after 4 hours, find their speed.

vaaruni | Student

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

htorrino | Student

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.