a school bus transported an excursion party to a picnic spot 150 km away .While returning it was raining and the bus has reduced it speed by 5 km per hour and it took one hour longer to make the return trip.Find the time taken to return.
Answers
6 hours is the time taken by the bus to return.
Step-by-step explanation:
Given that,
Distance = 150 Km
To find,
Time taken to return = ?
Procedure:
Let the actual speed of the bus be x km/hr
so,
The time taken = 150/x hour
A.T.Q.
While returning the speed reduced by = 5 Km/hr
so,
speed = x - 5 km/hr
Thus,
The time taken = 150/(x - 5) Km/hr
A.T.Q.
150/(x - 5) - 150/x = 1
⇒ 150(1/(x-5) - 1/x) = 1
⇒ 150[(x-x-5)/x(x-5)] = 1
⇒ (1500 * 5)/(x^2 - 5x) = 1
⇒ x^2 - 5x = 750
⇒ x^2 - 30x + 25x - 750 = 0
⇒ x(x - 30) + 25(x - 30) = 0
⇒ (x - 30)(x + 25) = 0
∵ x = 30 and x = -25
so, x = 30 as negative cannot be possible.
Thus,
Speed of bus = 30 Km/hr
Reduced speed = 30 - 5
= 25 Km/hr
Now,
Time taken by bus to return
= distance/speed
= 150/25
= 6 hours
Thus, 6 hours is the time taken to return.
Learn more: Find the time taken
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