A bus moving at its usual speed covers distance between towns A and B which
are 550 km apart in 1 hour less than it takes to cover the same distance, when
it is raining and the bus has to reduce the speed by 5 km/h. Calculate the time
taken by the bus to cover the distance between A and B when it is raining.
Answers
Usual speed 55km/he
Rain speed 50km/hr
The time taken by the bus to cover the distance between A and B when it is raining is 11 hours.
Given: The distance between towns A and B = 550 Km
At usual speed, the distance is covered in 1 hour less. When it is raining and the bus has to reduce the speed by 5 km/h.
To Find: The time taken by the bus to cover the distance between A and B when it is raining.
Solution:
Let the speed of the bus in the usual condition be 'x' km/h.
The distance between towns A and B = 550 Km
So, the time is taken by the bus in usual condition = 550/x hr
Now, speed of the bus in rainy conditions = ( x - 5 ) km/h
So, the time taken by the bus in rainy conditions = 550 / ( x - 5 ) hr
According to the problem, it is said that at the usual speed, the distance is covered in 1 hour less than when it is raining. So, framing an equation, we get;
550/( x - 5 ) - 550/x = 1
⇒ 550x - 550x + 2750 = x² - 5x
⇒ x² - 5x - 2750 = 0
⇒ x² - 55x + 50x - 2750 = 0
⇒ x ( x - 55 ) + 50 ( x - 55 ) = 0
⇒ ( x - 55 ) ( x + 50 ) = 0
⇒ x = 55, - 50
As it is speed so it cannot be negative.
So, the speed of the bus in the usual condition is = 55 km/h
So, speed of the bus in rainy conditions = ( x - 5 ) = ( 55 - 50 ) km/h
= 50 km/h
So, time is taken by the bus in rainy conditions = 550 / 50 hr
= 11 hr
Hence, the time taken by the bus to cover the distance between A and B when it is raining is 11 hours.
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