Question

The passenger bus starts out and travels at 65 kilometers per hour. three hours later, a car starts out from the same place and overtakes the bus in 8 hours and 40 minutes. what is the rate of the car?

Answer 1

1 h = 60 min

40 min = 40 / 60 = 2 * 20 / ( 3 * 20 ) = 2 / 3 h

8 h 40 min = 8 h + 2 / 3 h = 8 * 3 / 3 + 2 / 3 = 24 / 3 - 2 / 3 = 26 / 3 h

3 h = 3 * 3 / 3 = 9 / 3 h


Car travel 8 h 40 min.


For this time the bus travel = 8 h 40 min + 3 h = 11 h 40 min = 8 h 40 min + 3 h = 26 / 3 h + 3 h = 26 / 3 h + 9 / 3 h = 35 / 3 h

The bus travel distance = 65 km / h * 11 h 40 min = 65 km / h * 35 / 3 h = 65 * 35 / 3 = 2275 / 3 = ( 2274 + 1 ) / 3 = 2274 / 3 + 1 / 3 = 758 + 1 / 3 km

Velocity of car = 758 km + 1 / 3 km * 8 h 40 min = ( 2275 / 3 km ) / ( 26 / 3 h ) = ( 2275 * 3 km ) / ( 26 / 3 h ) = 2275 / 26 = 87.5 km / h


Proof :

The bus travel 758 + 1 / 3 km

Car travel : 87.5 km / h * 8 h 40 min = 87.5 km / h * 8 h 40 min = ( 87.5 * 2 / 2 ) * ( 26 / 3 ) = ( 175 / 2 ) * ( 26 / 3 ) = 175 * 26 / ( 2 * 3 ) = 4550 / 6 = ( 4548 + 2 ) / 6 = 4548 / 6 + 2 / 6 = 758 + 2 / 6 = 758 + 2 / ( 2 * 3 ) = 758 + 1 / 3 km